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# Awesome maths
A curated list of awesome mathematics resources.
## Foundations of mathematics
### Set theory
* [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/)
* [Set Theory on Wikibooks](https://en.wikibooks.org/wiki/Set_Theory)
### 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)
* [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
* [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
### 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
### Homotopy type theory
* [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
### 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)
### 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
### 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)
* [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
### 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
### 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
### 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
## Analysis
### 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
* [From Calculus to Analysis](http://www.wright.edu/~steen.pedersen/teaching/Calculus2Analysis.pdf) - Steen Pedersen
* [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
* [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
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### Functional analysis
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### Differential equations
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### Measure theory
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## Combinatorics
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### Graph theory
## Geometry and topology
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Algebraic geometry
## Probability and statistics
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* [Statistical Learning Theory](https://web.stanford.edu/class/cs229t/notes.pdf) - Percy Liang
## Numerical Analysis
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## Computer algebra
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## Websites
### Learning platforms
* [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)
### 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)
* [Wolfram Mathworld](http://mathworld.wolfram.com/)
* [Planetmath](http://planetmath.org/)
### Books
* [Basics of Algebra, Topology, and Differential Calculus](http://www.cis.upenn.edu/~jean/math-basics.pdf) - Jean Gallier (University of Pennsylvania)
### Misc
* [Areas of mathematics on Wikipedia](https://en.wikipedia.org/wiki/Areas_of_mathematics)
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