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# Awesome maths
A curated list of awesome mathematics resources.
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## Foundations of mathematics
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### Set theory
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* [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
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* [Set Theory on the Stanford Encyclopedia of Philosophy ](http://plato.stanford.edu/entries/set-theory/ )
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* [Set Theory on Wikibooks ](https://en.wikibooks.org/wiki/Set_Theory )
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### Logic
* [Introduction to logic ](http://logic.stanford.edu/intrologic/chapters/cover.html ) - Michael Genesereth, Eric Kao (Stanford University)
* [An introduction to formal logic ](https://textbookequity.org/oct/Textbooks/Magnus_forallx.pdf ) - P.D. Magnus (University at Albany)
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* [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://ssdi.di.fct.unl.pt/~pb/cadeiras/lc/0102/lpl%20textbook.pdf ) - Jon Barwise, John Etchemendy
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* [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)
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* [Formal logic ](http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf ) - Miguel Palomino
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### 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 ](http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf ) - Michael Barr, Charles Wells
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### Homotopy type theory
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* [Homotopy type theory ](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf )
## 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
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### Algebraic number theory
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* [Introduction to Algebraic Number Theory ](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf )
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* [Introduction to Algebraic Number Theory ](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf ) - F. Oggier
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* [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)
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### Analytic number theory
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* [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)
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* [Analytic number theory - Lecture notes based on Davenport’ ](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf ) - Andreas Strömbergsson
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## Algebra
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### Abstract algebra
* [Introduction to Abstract Algebra ](https://people.creighton.edu/~dsm33733/MTH581/Introduction%20to%20Abstract%20Algebra.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)
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* [Algebraic methods ](http://www1.spms.ntu.edu.sg/~frederique/AA11.pdf ) - F. Oggier
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* [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
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### Group theory
* [Notes on Group Theory ](https://www2.bc.edu/~reederma/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
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### Linear algebra
* [Fundamentals of linear algebra ](http://www.math.ubc.ca/~carrell/NB.pdf ) - James B. Carrell
* [Linear algebra and matrices ](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://www.mathematik.uni-muenchen.de/~renesse/AP09/hefferon.pdf ) - Jim Hefferon
* [Linear algebra ](http://www.calpoly.edu/~jborzell/Courses/Year%2010-11/Fall%202010/Petersen-Linear_Algebra-Math_306.pdf ) - Peter Petersen
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### Ring theory
* [Foundations of Module and Ring Theory ](http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf ) - Robert Wisbauer (University of Düsseldorf)
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### Galois theory
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* [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
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## Analysis
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### Real analysis
* [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 ) - Jirí 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
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* [From Calculus to Analysis ](http://www.wright.edu/~steen.pedersen/teaching/Calculus2Analysis.pdf ) - Steen Pedersen
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* [Real analysis for graduate students ](http://homepages.uconn.edu/~rib02005/rags010213.pdf ) - Richard F. Bass
* [Modern Real Analysis ](http://www.indiana.edu/~mathwz/PRbook.pdf ) - William P. Ziemer (Indiana University)
### Harmonic analysis
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* [Harmonic Analysis Lecture Notes ](http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf ) - Richard S. Laugesen (University of Illinois at Urbana–
* [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
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### Complex analysis
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* [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://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
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### Functional analysis
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* [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
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### Measure theory
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* [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’
* [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
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### Ordinary Differential Equations
* [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
### Partial differential equations
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* [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)
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## Combinatorics
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* [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
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### Graph theory
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* [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
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## Geometry and topology
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Algebraic geometry
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## Probability and statistics
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* [Statistical Learning Theory ](https://web.stanford.edu/class/cs229t/notes.pdf ) - Percy Liang
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## Numerical Analysis
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## Computer algebra
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# Websites
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## Learning platforms
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* [Khan Academy ](https://www.khanacademy.org/math )
* [Coursera ](https://www.coursera.org/courses?query=mathematics&languages=en )
* [Wikibooks ](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf )
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## Questions and answers
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* [Mathematics Stack Exchange ](http://math.stackexchange.com/ )
* [MathOverflow ](http://mathoverflow.net/ ) - for professional mathematicians
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## Encyclopedia
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* [Encyclopedia of Mathematics ](https://www.encyclopediaofmath.org )
* [Wolfram Mathworld ](http://mathworld.wolfram.com/ )
* [Planetmath ](http://planetmath.org/ )
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## Misc
* [Areas of mathematics on Wikipedia ](https://en.wikipedia.org/wiki/Areas_of_mathematics )
# Books
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* [Basics of Algebra, Topology, and Differential Calculus ](http://www.cis.upenn.edu/~jean/math-basics.pdf ) - Jean Gallier (University of Pennsylvania)
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# Online courses and MOOCs
# Videos
