awesome-math/README.md

# Awesome Math [![Awesome](https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg)](https://github.com/sindresorhus/awesome)

A curated list of awesome mathematics resources.

# Contents

<!-- START_TOC -->

* [Contents](#contents)
* [General Resources](#general-resources)
    * [Learning Platforms](#learning-platforms)
    * [Learn to Learn](#learn-to-learn)
    * [Youtube Series](#youtube-series)
    * [Tools](#tools)
    * [Questions and Answers](#questions-and-answers)
    * [Encyclopedia](#encyclopedia)
    * [Books](#books)
    * [Blogs](#blogs)
    * [Misc](#misc)
* [Lecture Notes](#lecture-notes)
    * [Foundations of Mathematics](#foundations-of-mathematics)
        * [Set Theory](#set-theory)
        * [Logic](#logic)
        * [Category Theory](#category-theory)
        * [Type Theory](#type-theory)
        * [Homotopy Type Theory](#homotopy-type-theory)
        * [Surreal Numbers](#surreal-numbers)
    * [Number Theory](#number-theory)
        * [Algebraic Number Theory](#algebraic-number-theory)
        * [Analytic Number Theory](#analytic-number-theory)
    * [Algebra](#algebra)
        * [Abstract Algebra](#abstract-algebra)
        * [Group Theory](#group-theory)
        * [Linear Algebra](#linear-algebra)
        * [Ring Theory](#ring-theory)
        * [Galois Theory](#galois-theory)
        * [Lie Algebras](#lie-algebras)
    * [Combinatorics](#combinatorics)
        * [Graph Theory](#graph-theory)
    * [Geometry and Topology](#geometry-and-topology)
        * [Differential Geometry](#differential-geometry)
        * [Algebraic Geometry](#algebraic-geometry)
        * [Topology](#topology)
        * [Algebraic Topology](#algebraic-topology)
    * [Analysis](#analysis)
        * [Real Analysis](#real-analysis)
        * [Harmonic Analysis](#harmonic-analysis)
        * [Complex Analysis](#complex-analysis)
        * [Functional Analysis](#functional-analysis)
        * [Measure Theory](#measure-theory)
        * [Ordinary Differential Equations](#ordinary-differential-equations)
        * [Partial Differential Equations](#partial-differential-equations)
    * [Probability and Statistics](#probability-and-statistics)
        * [Probability Theory](#probability-theory)
        * [Statistics](#statistics)
        * [Statistical Learning](#statistical-learning)
        * [Stochastic processes](#stochastic-processes)
    * [Numerical Analysis](#numerical-analysis)
    * [Signal processing](#signal-processing)
    * [Mathematics for Computer Science](#mathematics-for-computer-science)
    * [Mathematical Biology](#mathematical-biology)
    * [Mathematical Physics](#mathematical-physics)
* [License](#license)

<!-- END_TOC -->

# General Resources

## Learning Platforms

* [Khan Academy](https://www.khanacademy.org/math)
* [Coursera](https://www.coursera.org/courses?query=mathematics&languages=en)
* [MIT OpenCourseWare](http://ocw.mit.edu/courses/mathematics/)
* [edX](https://www.edx.org/course/subject/math)
* [Brilliant](https://brilliant.org/courses/#math-foundational)
* [WooTube](https://misterwootube.com/)
* [Mathigon](https://mathigon.org/)

## Learn to Learn

* [Understanding Mathematics](https://github.com/nelson-brochado/understanding-math)

## Youtube Series

* [Brandon Foltz](https://www.youtube.com/user/BCFoltz/playlists?view=1&sort=da&flow=grid)
* [3blue1brown](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/playlists)
* [NPTEL](https://www.youtube.com/watch?v=VVYLpmKRfQ8&list=PL6C92B335BD4238AB)
* [Prof. Leonard](https://www.youtube.com/watch?v=9FtHB7V14Fo&list=PL5102DFDC6790F3D0)
* [Crash Course](https://www.youtube.com/watch?v=zouPoc49xbk&list=PL8dPuuaLjXtNM_Y-bUAhblSAdWRnmBUcr)
* [Harvard](https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo)
* [MIT](https://www.youtube.com/watch?v=VPZD_aij8H0&list=PLUl4u3cNGP60uVBMaoNERc6knT_MgPKS0)

## Tools

* [Symbolab](https://www.symbolab.com/)
* [Desmos](https://www.desmos.com/calculator)
* [Math Words](http://www.mathwords.com/)
* [Wolfram Alpha](http://www.wolframalpha.com/)
* [Sympy](https://www.sympy.org/)
* [Sagemath](http://www.sagemath.org/)
* [Unit Converter](https://unitconverter.net)

## Questions and Answers

* [Mathematics Stack Exchange](http://math.stackexchange.com/)
* [MathOverflow](http://mathoverflow.net/) - for professional mathematicians

## Encyclopedia

* [Encyclopedia of Mathematics](https://www.encyclopediaofmath.org)
* [Planetmath](http://planetmath.org/)
* [ProofWiki](https://proofwiki.org/wiki/Main_Page)
* [Wolfram Mathworld](http://mathworld.wolfram.com/)

## Books

* [Calculus: Basic Concepts for High Schools](https://archive.org/details/TarasovCalculus) - L.V. Tarasov
* [Basics of Algebra, Topology, and Differential Calculus](http://www.cis.upenn.edu/~jean/math-basics.pdf) - Jean Gallier (University of Pennsylvania)
* [Multivariable Calculus](http://people.math.gatech.edu/%7Ecain/notes/calculus.html) - G. Cain, J. Herod (Georgia Tech)
* [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf)
* [Online Mathematics Textbooks](https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html)
* [Beginning and Intermediate Algebra](http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf)
* [Free Mathematics Books](https://github.com/EbookFoundation/free-programming-books/blob/master/free-programming-books.md#mathematics)
* [Trigonometry](http://www.mecmath.net/trig/trigbook.pdf)

## Blogs

* [BetterExplained](https://betterexplained.com/) - Maintained by Kalid Azad
* [ILoveMaths](http://ilovemaths.com/) - For grades 6 thru 12 in K-12 system
* [3blue1brown](https://www.3blue1brown.com/) - Animated Maths
* [Mathsisfun](https://www.mathsisfun.com) simple text light weight site for students upto highschool
* [MathematicsIsAScience](https://calculus123.com/wiki/Peter_Saveliev) - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA)

## Misc
* [Areas of mathematics on Wikipedia](https://en.wikipedia.org/wiki/Areas_of_mathematics)
* [Paul's Online Math Notes](http://tutorial.math.lamar.edu/) - Paul Dawkins (Lamar University)
* [List of electronic textbooks](http://faculty.atu.edu/mfinan/nnotes.html) - Marcel B. Finan (Arkansas Tech University)
* [Topology Atlas](http://at.yorku.ca/topology/)
* [Recreations in Math](http://djm.cc/library/Recreations_in_Mathematics_Licks_edited.pdf) - H. E. Licks (1917)
* [Magic Squares and Cubes](http://djm.cc/library/Magic_Squares_Cubes_Andrews_edited.pdf) - W. S. Andrews (1917)
* [Convex Optimization](https://web.stanford.edu/~boyd/cvxbook/) - Stephen Boyd and Lieven Vandenberghe

# Lecture Notes

## Foundations of Mathematics

* [Basic Concepts of Mathematics](http://www.trillia.com/zakon1.html) - Elias Zakon

### Set Theory

* [Sets, Relations, Functions](http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.html) - Ivo Düntsch, Günther Gediga
* [An Introduction to Set Theory](http://www.math.toronto.edu/weiss/set_theory.pdf) - William A. R. Weiss
* [Set Theory and Foundations of Mathematics](http://www.settheory.net/) - Sylvain Poirier
* [Set Theory on the Stanford Encyclopedia of Philosophy](http://plato.stanford.edu/entries/set-theory/)

### Logic

* [Introduction to Logic](http://logic.stanford.edu/intrologic/secondary/index.html) - Michael Genesereth, Eric Kao (Stanford University)
* [An Introduction to Formal Logic](https://www.fecundity.com/codex/forallx.pdf) - P.D. Magnus (University at Albany)
* [A Problem Course in Mathematical Logic](http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf) - Stefan Bilaniuk (Trent University)
* [Language, Proof, and Logic](http://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf) - Jon Barwise, John Etchemendy
* [Mathematical Logic](http://www.mathematik.uni-muenchen.de/~schwicht/lectures/logic/ws03/ml.pdf) - Helmut Schwichtenberg
* [Mathematical Logic](http://www.personal.psu.edu/t20/notes/logic.pdf) - Stephen G. Simpson (Pennsylvania State University)
* [Formal Logic](http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf) - Miguel Palomino
* [Predictive Arithmetic](https://web.math.princeton.edu/~nelson/books/pa.pdf) - Edward Nelson
* [Proofs and Concepts: the fundamentals of abstract mathematics](http://people.uleth.ca/~dave.morris/books/proofs+concepts.html) - Joy Morris, Dave Morris
* [Mathematical Reasoning: Writing and Proof](https://www.tedsundstrom.com/mathreasoning) - Ted Sundstrom
* [Logic and Proof](http://leanprover.github.io/logic_and_proof/) -  Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn

### Category Theory

* [Introduction to Category Theory and Categorical Logic](http://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf) - Thomas Streicher
* [An Introduction to Category Theory](http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf) - Harold Simmons
* [Category Theory](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.211.4754&rep=rep1&type=pdf) - Steve Awodey (Carnegie Mellon University)
* [Category Theory](http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf) - B. Pareigis
* [Category Theory for Computing Science](https://web.archive.org/web/20181221233252/http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf) - Michael Barr, Charles Wells
* [Toposes, Triples and Theories](http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf) - Michael Barr, Charles Wells
* [Abelian Categories](http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html) - Peter Freyd
* [Categories and Groupoids](http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html) - P. J. Higgins
* [Basic Concepts of Enriched Category Theory](http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html) - G. M. Kelley
* [Abstract and Concrete Categories: The Joy of Cats](http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html) - Jiri Adamek, Horst Herrlich, George Strecker
* [Seven Sketches in Compositionality: An Invitation to Applied Category Theory](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf) - Brendan Fong and David I. Spivak (MIT)

### Type Theory
* [Proofs and Types](http://www.paultaylor.eu/stable/prot.pdf) - Jean-Yves Girard
* [Intuitionistic Type Theory](https://archive-pml.github.io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf) - Per Martin-Lof
* [Type Theory and Functional Programming](https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) - Simon Thompson

### Homotopy Type Theory

* [Homotopy Type Theory](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf)

### Surreal Numbers

* [Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness](http://www.math.harvard.edu/~knill/teaching/mathe320_2015_fall/blog15/surreal1.pdf) - D. E. Knuth
* [An Introduction to Surreal Numbers](https://www.whitman.edu/Documents/Academics/Mathematics/Grimm.pdf) - Gretchen Grimm
* [Surreal Numbers and Games](http://web.mit.edu/sp.268/www/2010/surreal.pdf)
* [Conway names, the simplicity hierarchy and the surreal number tree](http://www.ohio.edu/people/ehrlich/ConwayNames.pdf) - Philip Ehrlich


## Number Theory

* [Elementary Number Theory: Primes, Congruences, and Secrets](http://wstein.org/ent/ent.pdf) - William Stein
* [Elementary Number Theory](http://www.iiserpune.ac.in/~ayan/MTH312/%28127%29.pdf) - W. Edwin Clark (University of South Florida)
* [A Course on Number Theory](http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf) - Peter J. Cameron
* [A Computational Introduction to Number Theory and Algebra](http://shoup.net/ntb/ntb-v2.pdf) - Victor Shoup
* [Number Theory: A Contemporary Introduction](http://math.uga.edu/~pete/4400FULL.pdf) - Pete L. Clark
* [An Introduction to the Theory of Numbers](http://www.trillia.com/moser-number.html) - Leo Moser
* [Yet Another Introductary Number Theory Textbook](https://www.poritz.net/jonathan/share/yaintt/) - Jonathan A. Poritz
* [Elementary Number Theory](https://napocaro.files.wordpress.com/2015/02/david_m-_burton_elementary_number_theory_sixth_bookfi-org.pdf) - David M. Burton

### Algebraic Number Theory

* [Introduction to Algebraic Number Theory](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf)
* [Introduction to Algebraic Number Theory](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf) - F. Oggier
* [Algebraic Number Theory](http://www.jmilne.org/math/CourseNotes/ANT.pdf) - J.S. Milne
* [Algebraic Number Theory Course Notes](http://people.math.gatech.edu/~mbaker/pdf/ANTBook.pdf) - Matthew Baker (Georgia Tech)
* [A Course In Algebraic Number Theory](http://www.math.uiuc.edu/~r-ash/ANT.html) - Robert Ash

### Analytic Number Theory

* [Introduction to Analytic Number Theory](http://www.math.uiuc.edu/~hildebr/ant/main.pdf) - A.J. Hildebrand (University of Illinois)
* [Elements of Analytic Number Theory](http://math.nsc.ru/~vdovin/lectures/numth_eng.pdf) - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
* [Analytic Number Theory](http://www.mathematik.uni-muenchen.de/~forster/v/ann/annth_all.pdf) - Otto Forster (LMU Munich)
* [Analytic Number Theory - Lecture Notes based on Davenport’s book](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf) - Andreas Strömbergsson


## Algebra

* [A Course in Universal Algebra](http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html) - S. Burris, H.P. Sankappanavar
* [A Course in Commutative Algebra](https://faculty.math.illinois.edu/~r-ash/ComAlg.html) - Robert Ash
* [First Course in Algebra](http://djm.cc/library/First_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910)
* [Second Course in Algebra](http://djm.cc/library/Second_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1911)
* [Algebra: An Elementary Text-Book, Part I](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf) - G. Chrystal (1904)
* [Algebra: An Elementary Text-Book, Part II](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_II_Chrystal_edited02.pdf) - G. Chrystal (1900)

### Abstract Algebra

* [Introduction to Abstract Algebra](https://zodml.org/sites/default/files/Introduction_to_Abstract_Algebra_0.pdf) - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University)
* [Introduction to Modern Algebra](http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf) - David Joyce (Clark University)
* [Algebraic Methods](http://www1.spms.ntu.edu.sg/~frederique/AA11.pdf) - F. Oggier
* [Abstract Algebra : Theory and Applications](http://abstract.ups.edu/download/aata-20150812.pdf) - Thomas W. Judson, Robert A. Beezer (Austin State University)
* [An Undergraduate Course in Abstract Algebra](http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf) - Robert Howlett
* [Elements of Abstract and Linear Algebra](http://www.math.miami.edu/~ec/book) - E.H. Connell (University of Miami)
* [Abstract Algebra: The Basic Graduate Year](http://www.math.uiuc.edu/~r-ash/Algebra.html) - Robert Ash
* [Abstract Algebra: Harvard Extension (Archived)](https://web.archive.org/web/20150528171650/extension.harvard.edu/open-learning-initiative/abstract-algebra) - Benedict Gross
* [Abstract Algebra: Harvard Extension Videos](https://www.youtube.com/playlist?list=PLA58AC5CABC1321A3) - Benedict Gross

### Group Theory

* [Notes on Group Theory](https://www2.bc.edu/mark-reeder/Groups.pdf) - Mark Reeder
* [Group Theory](http://www.jmilne.org/math/CourseNotes/GT.pdf) - J.S. Milne
* [Notes on Finite Group Theory](http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf) - Peter J. Cameron
* [Group Theory](http://www.cns.gatech.edu/GroupTheory/index.html) - Pedrag Civitanovic

### Linear Algebra

* [Fundamentals of Linear Algebra](http://www.math.ubc.ca/~carrell/NB.pdf) - James B. Carrell
* [Linear Algebra and Matrices](https://web.archive.org/web/20140824074655/http://mathstat.helsinki.fi/~fluch/linear_algebra_1-sp07/la1.pdf) - Martin Fluch
* [Vector Space Theory](http://www.maths.usyd.edu.au/u/bobh/UoS/MATH2902/vswhole.pdf) - Robert Howlett
* [Linear Algebra](http://joshua.smcvt.edu/linearalgebra) - Jim Hefferon
* [Linear Algebra](http://www.calpoly.edu/~jborzell/Courses/Year%2010-11/Fall%202010/Petersen-Linear_Algebra-Math_306.pdf) - Peter Petersen
* [MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks](https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06) - Juan Klopper
* [Linear Algebra](http://joshua.smcvt.edu/linalg.html) - Jim Hefferon
* [Elementary Linear Algebra](http://www.numbertheory.org/book/) - Keith Matthews
* [A First Courses in Linear Algebra](http://linear.ups.edu/) - Rob Breezer
* [Linear Algebra](https://www.math.ucdavis.edu/~linear/) - David Cherney, Tom Denton, Andrew Waldron
* [Introduction to vectors and tensors, Vol 1: linear and multilinear algebra](http://oaktrust.library.tamu.edu/handle/1969.1/2502) - Ray M Bowen, C. C. Wang
* [Introduction to vectors and tensors, Vol 2: vector and tensor analysis](http://oaktrust.library.tamu.edu/handle/1969.1/3609) - Ray M Bowen, C. C. Wang
* [Introduction to Applied Linear Algebra](https://web.stanford.edu/~boyd/vmls/vmls.pdf) - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)
* [Linear Algebra Done Wrong](https://www.math.brown.edu/~treil/papers/LADW/LADW_2017-09-04.pdf) - Sergei Treil
* [Immersive Linear Algebra](http://immersivemath.com/ila/index.html) - J. Ström, K. Åström, and T. Akenine-Möller
* [Interactive Linear Algebra](https://textbooks.math.gatech.edu/ila/) - Dan Margalit and Joseph Rabinoff
* [Linear Algebra, Infinite Dimensions, and Maple](https://people.math.gatech.edu/~herod/Hspace/Hspace.html) - James Herod

### Ring Theory

* [Foundations of Module and Ring Theory](http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf) - Robert Wisbauer (University of Düsseldorf)

### Galois Theory

* [An Introduction to Galois Theory](http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf) - Andrew Baker (University of Glasgow)
* [Fields and Galois Theory](http://www.jmilne.org/math/CourseNotes/FT.pdf) - J.S. Milne
* [Galois theory](http://homepages.warwick.ac.uk/~masda/MA3D5/Galois.pdf) - Miles Reid
* [Galois Theory](https://math.illinoisstate.edu/schebol/teaching/407-14-files/Stewart-galois_theory.pdf) - Ian Stewart

### Lie Algebras

* [Lie Algebras](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) - Shlomo Sternberg

## Combinatorics

* [Basic Combinatorics](http://www.math.utk.edu/~wagner/papers/comb.pdf) - Carl G. Wagner (University of Tennessee)
* [Applied Combinatorics](http://people.math.gatech.edu/~trotter/book.pdf) - Mitchel T. Keller, William T. Trotter
* [Notes on Combinatorics](http://www.maths.qmul.ac.uk/~pjc/notes/comb.pdf) - Peter J. Cameron
* [Analytic Combinatorics](http://algo.inria.fr/flajolet/Publications/book.pdf) - Philippe Flajolet, Robert Sedgewick
* [generatingfunctionology](http://www.math.upenn.edu/~wilf/DownldGF.html) - Herbert Wilf

### Graph Theory

* [Graph Theory: Lecture Notes](http://www.personal.psu.edu/cxg286/Math485.pdf) - Christopher Griffin
* [Graph Theory](http://www.cs.unibo.it/babaoglu/courses/cas00-01/tutorials/GraphTheory.pdf) - Reinhard Diestel


## Geometry and Topology

* [Fundamentals of Geometry](http://polly.phys.msu.ru/~belyaev/geometry.pdf) - Oleg A. Belyaev
* [A=B](https://www.math.upenn.edu/~wilf/AeqB.html) - M. Petkovsek, H. Wilf, D. Zeilberger
* [Elements](http://aleph0.clarku.edu/~djoyce/java/elements/toc.html) - Euclid
* [Euclid's Elements Redux](http://starrhorse.com/euclid/) - Daniel Callahan
* [Mathematical Illustrations](http://www.math.ubc.ca/~cass/graphics/manual/) - Bill Casselman
* [Byrne's Euclid](https://www.c82.net/euclid/) - Oliver Byrne
* [Plane Geometry](http://djm.cc/library/Plane_Geometry_Wentworth_Smith_edited.pdf) - George Wentworth and David Eugene Smith (1913)
* [Planes and Spherical Trigonometry](http://djm.cc/library/Plane_Spherical_Trigonometry_Wentworth_Smith_edited_2.pdf) - George Wentworth and David Eugene Smith (1915)
* [Coordinate Geometry](http://djm.cc/library/Coordinate_Geometry_Fine_Thompson_edited03.pdf) - Henry Buchard Fine and Henry Dallas Thompson (1911)
* [Analytic Geometry](http://djm.cc/library/Analytic_Geometry_Siceloff_Wentworth_Smith_edited.pdf) - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (1922)

### Differential Geometry

* [Introduction to Differential Geometry](https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf) - Joel W. Robbin, Dietmar A. Salamon
* [Notes on Differential Geometry and Lie Groups](http://www.seas.upenn.edu/~jean/diffgeom.pdf) - Jean Gallier (University of Pennsylvania)
* [Topics in Differential Geometry](http://www.mat.univie.ac.at/~michor/dgbook.pdf) - Peter W. Michor
* [Lectures on Differential Geometry](http://mysite.science.uottawa.ca/rossmann/Differential%20Geometry%20book_files/Diffgeo.pdf) - Wulf Rossmann
* [An Introduction to Riemannian Geometry](http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf) - Sigmundur Gudmundsson (Lund University)
* [The Geometry and Topology of Three-Manifolds](http://msri.org/publications/books/gt3m/) - W. Thurston
* [Semi-Riemann Geometry and General Relativity](http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf) - Shlomo Sternberg

### Algebraic Geometry

* [A Brief Introduction to Algebraic Geometry](http://www.sci.ccny.cuny.edu/~ksda/PostedPapers/rickksda1107.pdf) - R.C. Churchill
* [Introduction to Algebraic Geometry](http://www.math.lsa.umich.edu/~idolga/631.pdf) - Igor V. Dolgachev
* [Foundations of Algebraic Geometry](http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf) - Ravi Vakil
* [Algebraic Geometry](http://www.cis.upenn.edu/~jean/algeoms.pdf) - Jean Gallier, Stephen S. Shatz (University of Pennsylvania)
* [Algebraic Geometry](http://www.jmilne.org/math/CourseNotes/AG.pdf) - J.S. Milne
* [Algebraic Geometry](http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf) - Andreas Gathmann (University of Kaiserslautern)
* [The Stacks Project](https://stacks.math.columbia.edu/) - Maintained by Aise Johan de Jong (Columbia)

### Topology

* [Elementary Applied Topology](https://www.math.upenn.edu/~ghrist/notes.html) - Robert Ghrist (UPenn)
* [Introduction to Topology](http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf)
* [Introduction to Topology](http://www.math.bme.hu/~kalex/Teaching/Spring10/Topology/TopNotes_Spring10.pdf) - Alex Küronya
* [Introductory Topology](http://www.math.clemson.edu/~jimlb/Teaching/2009-10/Math986/Topology.pdf) - Jim L. Brown
* [General Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/Topo.pdf) - Pierre Schapira (Paris VI University)
* [Elementary Topology Problem Textbook](http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf)
* [General Topology](http://www.math.ku.dk/~moller/e03/3gt/notes/gtnotes.pdf) - Jesper M. Møller

### Algebraic Topology

* [Algebraic Topology](http://www.math.cornell.edu/~hatcher/AT/AT.pdf) - Allen Hatcher
* [A Concise Course in Algebraic Topology](http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf) - J. P. May
* [Introduction to Algebraic Topology](http://www.math.muni.cz/~cadek/at/at.pdf) - Martin Cadek
* [Algebra and Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/AlTo.pdf) - Pierre Schapira (Paris VI University)
* [Lecture Notes in Algebraic Topology](http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf) - James F. Davis, Paul Kirk (Indiana University)
* [Algebraic Topology](https://www.ma.utexas.edu/ibl1/courses/resources/12_15_07_grad_alg_top_mooremethod.pdf) - Michael Starbird
* [Lecture Notes on Algebraic Topology](http://www.math.nus.edu.sg/~matwujie/ma5209.pdf) - Jie Wu


## Analysis

### Real Analysis

* [MIT OpenCourseWare Lectures on Calculus](https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/) - G. Strang
* [Elementary Calculus: An Approach Using Infinitesimals](http://www.math.wisc.edu/~keisler/calc.html) - Professor H. Jerome Keisler
* [An Introduction to Real Analysis](https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf) - John K. Hunter (University of California at Davis)
* [Introduction to Real Analysis](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF) - William F. Trench (Trinity University, Texas)
* [Basic Analysis: Introduction to Real Analysis](http://www.jirka.org/ra/realanal.pdf) - Jiří Lebl
* [Elementary Real Analysis](http://prac.im.pwr.wroc.pl/~kwasnicki/pl/stuff/tbb-hyper.pdf) - Thomson, Bruckner
* [Lecture Notes in Real Analysis](http://ms.mcmaster.ca/~sawyer/Publications/Real_Analysis.pdf) - Eric T. Sawyer (McMaster University)
* [Real Analysis](http://math.harvard.edu/~ctm/papers/home/text/class/harvard/212a/course/course.pdf) - C. McMullen
* [Real Analysis for Graduate Students](http://bass.math.uconn.edu/3rd.pdf) - Richard F. Bass
* [Modern Real Analysis](http://www.math.purdue.edu/~torres/pubs/Modern-real-analysis.pdf) - William P. Ziemer (Indiana University)
* [Mathematical Analysis Vol I](http://www.trillia.com/zakon-analysisI.html) - Elias Zakon
* [Mathematical Analysis Vol II](http://www.trillia.com/zakon-analysisII.html) - Elias Zakon
* [Advanced Calculus](http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf) - Lynn Loomis, Schlomo Sternberg
* [ Analysis of Functions of a Single Variable](http://spot.colorado.edu/~baggett/analysis.html) - Lawerence Baggett
* [The Calculus of Functions of Several Variables](http://www.synechism.org/wp/the-calculus-of-functions-of-several-variables/) - Dan Sloughter
* [A ProblemText in Advanced Calculus](http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf) - John M. Erdman
* [Calculus and Linear Algebra. Vol. 1](http://hdl.handle.net/2027/spo.5597602.0001.001) - Wilfred Kaplan, Donald J. Lewis
* [Calculus and Linear Algebra. Vol. 2](https://quod.lib.umich.edu/s/spobooks/5597602.0002.001) - Wilfred Kaplan, Donald J. Lewis
* [Introduction to Calculus I and II](http://www.math.odu.edu/~jhh/counter10.html) - J.H. Heinbockel
* [Active Calculus](http://faculty.gvsu.edu/boelkinm/Home/Active_Calculus.html) - Matt Boelkins
* [Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis"](https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin) - George M. Bergman
* [Calculus Made Easy](http://calculusmadeeasy.org/) - Silvanus P. Thompson (1910)
* [Elements of Differential and Integral Calculus](http://djm.cc/library/Elements_Differential_Integral_Calculus_Granville_edited_2.pdf) - William Anthony Granville (1911)

### Harmonic Analysis

* [Harmonic Analysis Lecture Notes](http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf) - Richard S. Laugesen (University of Illinois at Urbana–Champaign)
* [Harmonic Analysis](http://www.math.uchicago.edu/~schlag/harmonicnotes.pdf) - W. Schlag
* [Lecture Notes: Fourier Transform and its Applications](https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf) - Brad Osgood
* [Fourier Analysis](http://www.reed.edu/physics/courses/Physics331.f08/pdf/Fourier.pdf) - Lucas Illing

### Complex Analysis

* [Introduction to Complex Analysis](http://www.unc.edu/math/Faculty/met/complex.pdf) - Michael Taylor
* [An Introduction to Complex Analysis and Geometry](http://www.math.uiuc.edu/~jpda/jpd-complex-geometry-book-5-refs-bip.pdf) - John P. D'Angelo (University of Illinois)
* [A First Course in Complex Analysis](http://math.sfsu.edu/beck/papers/complex.pdf) - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
* [A Guide to Complex Variables](http://www.math.wustl.edu/~sk/books/guide.pdf) - Steven G. Krantz
* [Complex Analysis](http://www.maths.manchester.ac.uk/~cwalkden/complex-analysis/complex_analysis.pdf) - Charles Walkden
* [Complex Analysis](http://www.math.ku.dk/noter/filer/koman-12.pdf) - Christian Berg
* [Complex Variables](http://people.math.sc.edu/girardi/m7034/book/AshComplexVariablesWithHyperlinks.pdf) - R. B. Ash, W.P. Novinger
* [Complex Analysis](http://www.maths.lth.se/matematiklu/personal/olofsson/CompHT06.pdf) - Christer Bennewitz
* [Complex Analysis](https://web.archive.org/web/20150620124453/https://www.math.washington.edu/~marshall/math_536/Notes.pdf) - Donald E. Marshall
* [A Concise Course in Complex Analysis and Riemann Surfaces](http://www.math.uchicago.edu/~schlag/bookweb.pdf) - Wilhelm Schlag
* [Complex Analysis](http://people.math.gatech.edu/%7Ecain/winter99/complex.html) - G. Cain (Georgia Tech)
* [Complex Analysis](https://complex-analysis.com/) - Juan Carlos Ponce Campuzano

### Functional Analysis

* [An Introduction to Functional Analysis](http://www.math.uwaterloo.ca/~lwmarcou/Preprints/LinearAnalysis.pdf) - Laurent W. Marcoux (University of Waterloo)
* [Functional Analysis: Lecture Notes](http://users.math.msu.edu/users/jeffrey/920/920notes.pdf) - Jeff Schenker (Michigan State University)
* [Functional Analysis Lecture Notes](http://www.math.hkbu.edu.hk/~zeng/Teaching/math3680/FAnotes.pdf) - T.B. Ward (University of East Anglia)
* [Functional Analysis](http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf) - Alexander C. R. Belton
* [Topics in Real and Functional Analysis](https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdf) - Gerald Teschl
* [Functional Analysis](http://www2.math.ou.edu/~cremling/teaching/lecturenotes/fa-new/LN-I.pdf) - Christian Remling
* [Theory of Functions of a Real Variable](http://www.math.harvard.edu/~shlomo/docs/Real_Variables.pdf) - Shlomo Sternberg
* [Functional Analysis](http://spot.colorado.edu/~baggett/functional.html) - Lawerence Baggett

### Measure Theory

* [An Introduction to Measure Theory](https://terrytao.files.wordpress.com/2011/01/measure-book1.pdf) - Terence Tao (UCLA)
* [Lecture Notes on Measure Theory and Functional Analysis](http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf) - P. Cannarsa, T. D’Aprile
* [Lecture Notes in Measure Theory](http://www.math.chalmers.se/~borell/MeasureTheory.pdf) - Christer Borell
* [A Crash Course on the Lebesgue Integral and Measure Theory](http://www.gold-saucer.org/math/lebesgue/lebesgue.pdf) - Steve Cheng
* [Measure Theory](https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf) - John K. Hunter (University of California at Davis)
* [Measure and Integration](https://people.math.ethz.ch/~salamon/PREPRINTS/measure.pdf) - Dietmar A. Salamon (ETH Zürich)
* [Lecture notes: Measure Theory](http://www.math.ucsd.edu/~bdriver/240-00-01/Lecture_Notes/measurep.pdf) - Bruce K. Driver

### Ordinary Differential Equations

* [Difference Equations To Differential Equations](http://www.synechism.org/wp/difference-equations-to-differential-equations/) - Dan Sloughter
* [Ordinary Differential Equation](https://www.math.uni-bielefeld.de/~grigor/odelec2008.pdf) - Alexander Grigorian (University of Bielefeld)
* [Ordinary Differential Equations: Lecture Notes](http://www.cs.bgu.ac.il/~leonid/ode_bio_files/Ionascu_LectNotes.pdf) - Eugen J. Ionascu
* [Ordinary Differential Equations](http://www.math.lmu.de/~philip/publications/lectureNotes/ODE.pdf) - Peter Philip
* [Ordinary Differential Equations](http://users.math.msu.edu/users/gnagy/teaching/ode.pdf) - Gabriel Nagy
* [Ordinary Differential Equations and Dynamical Systems](http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf) - Gerald Teschl
* [Notes on Differential Equations](http://leipper.org/manuals/zip-fill/dn-difeq-notes.pdf) - Bob Terrell
* [Elementary Differential Equations](http://digitalcommons.trinity.edu/mono/8/) - William F. Trench
* [Elementary Differential Equations With Boundary Value Problems](http://digitalcommons.trinity.edu/mono/9/) - William F. Trench
* [Notes on Diffy Qs: Differential Equations for Engineers](http://www.jirka.org/diffyqs/) - Jiří Lebl
* [Differential Equations](http://djm.cc/library/Differential_Equations_Phillips_edited.pdf) - H. B. Phillips (1922)

### Partial Differential Equations

* [Notes on Partial Differential Equations](https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf) - John K. Hunter (University of California at Davis)
* [Partial Differential Equations: Lecture Notes](http://www.math.uni-leipzig.de/~miersemann/pdebook.pdf) - Erich Miersemann (Leipzig University)
* [Linear Methods of Applied Mathematics](http://www.mathphysics.com/pde/) - E. Harrell, J. Herod (Georgia Tech)


## Probability and Statistics

### Probability Theory

* [Introduction to Probability](https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf) - Charles M. Grinstead, J. Laurie Snell
* [Introduction to Probability](http://vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf) - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)
* [A Short Introduction to Probability](http://www.maths.uq.edu.au/~kroese/asitp.pdf) - Dirk P. Kroese (University of Queensland)
* [Probability: Theory and Examples](https://www.math.duke.edu/~rtd/PTE/PTE4_1.pdf) - Rick Durrett
* [Probability and Statistics Cookbook](https://github.com/mavam/stat-cookbook/releases/download/0.2.3/stat-cookbook.pdf) - Matthias Vallentin (UC Berkeley)
* [The Only Probability Cheatsheet You'll Ever Need](http://www.wzchen.com/probability-cheatsheet/) - William Chen
* [An Introduction to Probability and Random Processes](http://www.ellerman.org/Davids-Stuff/Maths/Rota-Baclawski-Prob-Theory-79.pdf) - Gian-Carlo Rota, Kenneth Baclawski
* [Foundations of Constructive Probability Theory](https://arxiv.org/pdf/1906.01803.pdf) - Yuen-Kwok Chan

### Statistics

* [Lecture Notes on Statistical Theory](http://homepages.math.uic.edu/~rgmartin/Teaching/Stat411/Notes/411notes.pdf) - Ryan Martin (University of Illinois)
* [Introduction to Statistics and Data Analysis for Physicists](http://www-library.desy.de/preparch/books/vstatmp_engl.pdf) - Gerhard Bohm, Günter Zech
* [Probability and Mathematical Statistics](http://www.iiserpune.ac.in/~ayan/MTH201/Sahoo_textbook.pdf) - Prasanna Sahoo (University of Louisville)
* [Lectures on Statistics](http://math.arizona.edu/~faris/stat.pdf) - William G. Faris
* [Statistical Theory](http://pages.pomona.edu/~ajr04747/Fall2009/Math152/Notes/Math152NotesFall09.pdf) - Adolfo J. Rumbos
* [Theory of Statistics](http://mason.gmu.edu/~jgentle/books/MathStat.pdf) - James E. Gentle (George Mason University)
* [Theory of Statistics](http://math.arizona.edu/~jwatkins/notests.pdf) - Joseph C. Watkins (University of Arizona)
* [Glossary of Data Modeling](https://web.archive.org/web/20130523134625/http://www.aiaccess.net/e_gm.htm) - AI Access
* [Statistics Papers](http://www.ats.ucla.edu/stat/papers/) - List of statistics papers curated by the Institute for Digital Research and Education (IDRE) at UCLA on methods such as bootstrap and factor invariance.
* [NIST Handbook of Statistical Methods](http://itl.nist.gov/div898/handbook/index.htm) - Resource on practical statistics directed towards scientists and engineers.
* [Concepts and Applications of Inferential Statistics](http://vassarstats.net/textbook/) - Richard Lowry
* [Rough set data analysis: A road to non-invasive knowledge discovery](http://www.cosc.brocku.ca/~duentsch/papers/methprimer2.html) - Ivo Düntsch, Günther Gediga
* [Statistical Thinking for the 21st Century](https://statsthinking21.org/) - Russell A. Poldrack
* [Odds and Ends: Introducing Probability & Decision with a Visual Emphasis](https://jonathanweisberg.org/vip/) - Jonathan Weisberg
* [Seeing Theory](https://seeing-theory.brown.edu/) - Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang
* [Statistics Done Wrong](https://www.statisticsdonewrong.com/) - Alex Reinhart
* [All of Statistics: A Concise Course in Statistical Inference](https://link.springer.com/book/10.1007/978-0-387-21736-9) - Larry Wasserman

### Statistical Learning

* [An Introduction to Statistical Learning with Applications in R](http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf) - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
* [The Elements of Statistical Learning](http://web.stanford.edu/~hastie/Papers/ESLII.pdf) - Trevor Hastie, Robert Tibshirani, Jerome Friedman
* [Statistical Learning Theory](https://web.stanford.edu/class/cs229t/notes.pdf) - Percy Liang
* [Reinforcement Learning: An Introduction](https://webdocs.cs.ualberta.ca/~sutton/book/bookdraft2016sep.pdf) - Richard S. Sutton, Andrew G. Barto

### Stochastic processes

* [Lectures on Stochastic Processes](http://www.math.tifr.res.in/~publ/ln/tifr24.pdf) - K. Ito (Tata Institute of Fundamental Research, Bombay)
* [Probability and Stochastic Processes with Applications](http://www.math.harvard.edu/~knill/teaching/math144_1994/probability.pdf) - Oliver Knill (Harvard University)
* [Stochastic Processes](http://statweb.stanford.edu/~adembo/math-136/nnotes.pdf) - Amir Dembo (Stanford University)
* [Lecture Notes on Stochastic Processes](http://www.mi.fu-berlin.de/wiki/pub/CompMolBio/MarkovKetten15/stochastic_processes_2011.pdf) - Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin)
* [Introduction to Stochastic Processes - Lecture Notes](https://www.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf) - Gordan Žitković (University of Texas)
* [Applied Stochastic Processes in science and engineering](https://www.math.uwaterloo.ca/~mscott/Little_Notes.pdf) - Matt Scott (University of Waterloo)
* [An Introduction to Stochastic Processes in Continuous Time](http://www.math.leidenuniv.nl/~spieksma/colleges/sp-master/sp-hvz1.pdf) - Flora Spieksma (Leiden University)
* [Markov Chains and Mixing Times](http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf) - David A. Levin, Yuval Peres, Elizabeth L. Wilmer
* [Convergence of Stochastic Processes](http://www.stat.yale.edu/~pollard/Books/1984book/pollard1984.pdf) - David Pollard


## Numerical Analysis

* [Introduction to Numerical Analysis](http://www.math.umd.edu/~dlevy/books/na.pdf) - Doron Levy (University of Maryland)
* [A Concise Introduction to Numerical Analysis](http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf) - Douglas N. Arnold (University of Minnesota)
* [Numerical Analysis](http://people.cs.uchicago.edu/~ridg/newna/nalrs.pdf) - L. Ridgway Scott
* [Lectures In Basic Computational Numerical Analysis](http://www.engr.uky.edu/~acfd/egr537-lctrs.pdf) - J. M. McDonough (University of Kentucky)
* [Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods](http://www.math.uni-bremen.de/~schmidt/SS04/YSU_Notes.pdf) - Alfred Schmidt, Arsen Narimanyan
* [Numerical Analysis for Engineers](https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/) - Douglas Wilhelm Harder


## Signal processing

* [Introduction to Signal Processing](http://www.ece.rutgers.edu/~orfanidi/intro2sp/orfanidis-i2sp.pdf) - Sophocles J. Orfanidis (Rutgers University)
* [Foundations of Signal Processing](http://www.fourierandwavelets.org/FSP_v1.1_2014.pdf) - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal
* [An Introduction to Statistical Signal Processing](https://ee.stanford.edu/~gray/sp.pdf) - Robert M. Gray, Lee D. Davisson
* [Think DSP](https://greenteapress.com/wp/think-dsp/) - Allen B. Downey
* [Linear algebra, signal processing, and wavelets. A unified approach.](https://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v15/kompendium/applinalgpython.pdf) - Øyvind Ryan (University of Oslo)


## Mathematics for Computer Science

* [Mathematics for Computer Science](https://people.csail.mit.edu/meyer/mcs.pdf) - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
* [Algorithms and Complexity](http://www.math.upenn.edu/%7Ewilf/AlgComp3.html) - H. Wilf
* [Lecture Notes on Optimization](http://people.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf) - Pravin Varaiya
* [Information Theory, Inference, and Learning Algorithms](http://www.inference.org.uk/mackay/itila/book.html) - David J. C. MacKay
* [The Chaos Textbook: Mathematics in the age of the computer](https://hypertextbook.com/chaos/) - Glenn Elert

## Mathematical Biology

* [Mathematical Biology](http://www.math.ust.hk/~machas/mathematical-biology.pdf) - Jeffrey Chasnov

## Mathematical Physics

* [Introduction to Continuum Mechanics](http://oaktrust.library.tamu.edu/handle/1969.1/2501) - Ray. M. Bowen
* [Mathematical Tools for Physics](http://www.physics.miami.edu/nearing/mathmethods/) - James Nearing
* [Mechanism of the Heavens (1831)](http://www.malaspina.com/etext/heavens.htm) - Mary Somerville

# License

[![CC0](http://i.creativecommons.org/p/zero/1.0/88x31.png)](http://creativecommons.org/publicdomain/zero/1.0/)

To the extent possible under law, [Cyrille Rossant](http://cyrille.rossant.net) has waived all copyright and related or neighboring rights to this work.