Textbooks in Mathematics

• Basic Concepts of Mathematics by Elias Zakon
• Mathematical Analysis I by Elias Zakon
• Basic algebra and trigonometry. by Thomas Ward
• First Year Mathematics, (notes by William Chen)
• Multivariable Calculus by George Cain & James Herod
• Complex Analysis by George Cain
• Linear Algebra byJim Hefferon
• Elementary Linear Algebra by Keith Matthews.
• Measure Theory and Integration by V. Liskevich
• MEASURE THEORY by D.H.Fremlin plain tex sources
• Complex Analysis by Douglas N. Arnold
• Real Analysis for Engineers by Erhan Cinlar and Robert J. Vanderbei
• Set Theoretic Real Analysis by Krzysztof Ciesielski
• Expository notes by Daniel Allcock in The finite reflection groups
• Classical Geometry by Danny Calegari
• Classical Geometry and Low-Dimensional Topology by Danny Calegari
• Difference Equations to Differential Equations by Dan Sloughter
• Course of linear algebra and multidimensional geometry by Ruslan Sharipov
• Examples, Lecture Notes and Specimen Exam Questions and Natural Sciences Tripos
• Calculus project of Michael Livshits
• The Matrix Cookbook by Kaare Brandt Petersen
• The Octonions by John C. Baez

• Mathematical Logic - an Introduction by Michal Walicki
• Set theory by Dr. P. G. Dixon
• Mathematical Logic by Stephen G. Simpson
• Foundations of Mathematics by Stephen G. Simpson
• Model Theory by Stephen G. Simpson
• The theory of the foundations of mathematics - 1870 to 1940
• A Problem Course in Mathematical Logic by Stefan Bilaniuk
• Computability and Incompleteness by Jeremy Avigad
• Complete proofs of Gödel's Incompleteness Theorems
• Fundamentals of Model Theory by William Weiss and Cherie D'Mello
  For more logic lecture notes go to: ASSOCIATION FOR SYMBOLIC LOGIC members.
  For more set theory materials go to: Set Theory Preprint Sites

• Lecture Notes on Discrete Mathematics by László Lovász

• An Introduction to the Theory of Numbers by Leo Moser
• Elementary Number Theory by W. Edwin Clark
• Lecture notes on elementary number theory (Bruce Ikenaga)
• exercizes with solutions on elementary number theory (Nigel Byott)
• Naoki Sato's Number Theory Notes
• Math 780: Elementary Number Theory, Notes by Michael Filaseta, 1997

• Lecture notes on p-adic numbers (Andrew Baker)

• Draft of PCMI Lecture Notes on Open Questions in Arithmetic Algebraic Geometry (Alice Silverberg)

• William Hammond's Fermat Archive
• Notes on Fermat's Last Theorem, A.J. van der Poorten, Canadian Mathematical Society Series of Monographs and Advanced Texts, Wiley-Interscience, January, 1996, ISBN 0-471-06261-8
  • Review of Alf van der Poorten's Notes on Fermat's Last Theorem by Andrew Granville

•  A Computational Introduction to Number Theory and Algebra by Victor Shoup
• A Course In Algebraic Number Theory by Robert B. Ash
• Course Notes for elementary and algebraic number theory by Ivan Fesenko
• Course Notes by Jim Milne: Algebraic Number Theory
• Algebraic Number Theory, Course notes by Robin Chapman
• Invitation to higher local fields, by Ivan Fesenko and Masato Kurihara (editors)
• Survey of Euclidean Number Fields (ps file 371K) (Franz Lemmermeyer)
• Algebra and Number Theory by Andrew Baker
• Elementary Number Theory by William A. Stein
• Notes for Dick Gross' Algebraic Number Theory Course by S. Sather-Wagstaff
• Algebraic Number Theory & Introduction to Automorphic L-functions by Ching-Li Chai
• Lecture notes on Algebraic Number Theory by Jerome Hoffmann
• Introduction to Number Theory by Franz Lemmermeyer

• Distribution of Prime Numbers, Lecture notes by William Chen
• Course notes for analytic number theory (Graham Everest) (ps 442K)
• Introduction to Analytic Number Theory by Noam Elkies

• Lectures on Matrices by J. H. M. Wedderburn
• Elementary Abstract Algebra by Edwin Clark
• Intro to Abstract Algebra by Paul Garrett
• Elements of Abstract and Linear Algebra by Edwin H. Connell
• Abstract Algebra:The Basic Graduate Year by Robert Ash
• A Course In Commutative Algebra by Robert Ash
• Notes for geometric group theory course, by John R. Stallings
• Advanced Linear Algebra lecture notes by Keith Matthews (with real algorithm for the real Jordan form)
• Commutative algebra by Ivan Fesenko
• Abstract Algebra - Number Theory, Group Theory, Galois Theory by Daviidd Wilkins
• Workbook in Higher Algebra by David Surowski with index, many exercises
• Abstract group theory Papers and Notes by Chuck Miller
• The Classification of the Finite Simple Groups by Daniel Gorenstein, Richard Lyons, and Ronald Solomon
• Group Characters, Symmetric Functions, and the Hecke Algebra by David M. Goldschmidt
• Finite Groups and their Representations by Andrew Baker
• Classical Groups by Peter Cameron
• Galois theory by Miles Reid
• Toeplitz and Circulant Matrices by R. M. Gray

• Differential Algebra by Joseph Fels Ritt
• Structure and Representations of Jordan Algebras by Nathan Jacobson
• An Invitation to General Algebra and Universal Constructions, by George M. Bergman
• A Course in Universal Algebra by Stanley N. Burris and H.P. Sankappanavar
• Fundamental Problems in Algorithmic Algebra by Chee Yap
• Braid groups and Galois theory by Frazer Jarvis
• A. N. Whitehead's Universal Algebra by Stephen Blake
• Varieties of Lattices by Peter Jipsen and Henry Rose

• Algebraic geometry and projective differential geometry by Joseph M. Landsberg
• Introduction to Algebraic Geometry, Igor V. Dolgachev
• Notes on Algebraic Geometry, J.S. Milne.
• Undergraduate tutorial on modular forms by Marty Weissman
• Modular forms (Igor Dolgachev)
• Complex analytic and algebraic geometry - Jean-Pierre Demailly
• Moduli Spaces in Algebraic Geometry edited by L. Goettsche
• Algebraic Curves by Hendrik L. Lenstra
• Lectures by David A. Cox - Introduction to Algebraic Geometry, Minicourse on Toric Varieties, etc.
• Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg
• Lectures on Vanishing Theorems by Hélène Esnault, Eckart Viehweg
• Introduction to Algebraic Geometry by Ravi Vakil
• Algebra and Geometry in several complex variables by Victor Palamodov
• Determinantal rings by Winfried Bruns and Udo Vetter

• Elliptic curves by Miles Reid
• Elliptic curves, student project, Annegret Weng (ps 726K)
• Arithmetic on hyperelliptic curves, Annegret Weng (ps 148K)
• Course Notes by Jim Milne: Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology
• The Modular curves X₀(N), Lecture notes by Bas Edixhoven
• Expository articles - Computing rational points on curves, Elliptic curves by Bjorn Poonen

• A Gentle Introduction to Category Theory, by Maarten M.Fokkinga
• Mixed Motives by Marc Levine
• Chris Hillman's Eprints has a concise introduction to category theory.
• David Madore's Math Page has a 50 page treatise on categories, in DVI and PS.
• Lecture notes on Categories, Derived Categories, Homological Algebra by Pierre Schapira
• Toposes, Triples and Theories by Michael Barr and Charles Wells
• Higher-Dimensional Categories: an illustrated guide book by Eugenia Cheng and Aaron Lauda
• Abstract and Concrete Categories by J. Adamek, H. Herrlich, G. Strecker
• Higher Operads, Higher Categories by Tom Leinster

• Algebraic Groups and Discontinuous Subgroups by Armand Borel and George D. Mostow
• Theory of representations etc. by Claudio Procesi
• Semisimple Lie Algebras and their Representations, by Robert N. Cahn,
• Linear Algebraic Groups - minor thesis by David Dumas

 

• Textbook in Problems on Elementary Topology by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov and N.Y.Netsvetaev unfinished
• Topology Course Lecture Notes by Aisling McCluskey and Brian McMaster
• Topology lecture notes(3rd year) by Thomas Ward
• Foliations and the topology of 3-manifolds by Danny Calegari

• Allen Hatcher's homepage has a (nearly complete) textbook.
• Introduction to Sheaf Theory and Algebraic Topology, by Pierre Schapira
• Cohomology, Connections, Curvature and Characteristic Classes by David Mond
• Introduction to Characteritic Classes and Index Theory by Jean-Pierre Schneiders

• Algebraic Topology by Solomon Lefschetz, AMS 1942, 389 pp.
• Abstract group theory and topology articles by Walter Neumann

• An introduction to algebraic K-theory, by Charles Weibel.

• Classical Knot Theory by C. Kearton
• Knots Knotes. by J. D. Roberts
• Vassiliev invariants and combinatorial structures by S.V.Duzhin
• Introduction to Vassiliev knot invariants by S.Chmutov, S.Duzhin

• Homeomorphisms in Analysis by Casper Goffman, Togo Nishiura, and Daniel Waterman
• Why the Boundary of a Round Drop Becomes a Curve of Order Four by A. N. Varchenko and P. I. Etingof
• Lectures on Entire Functions by B. Ya. Levin
• Constructive Real Numbers and Constructive Function Spaces by N. A. Sanin
• Complex Variables by Robert B. Ash and W.P. Novinger
• Foundations of Nonstandard Analysis by Erland Gadde
• Analytic functions by Stanislaw Saks, Antoni Zygmund

• Functional Analysis by Douglas N. Arnold
• Paul Garrett's lecture notes
• Functional Analysis (3rd year) lecture notes by Thomas Ward
• Functional Analysis and Semi-Groups by Einar Hille and R. S. Phillips, AMS 1957, 808 pp
• The Convenient Setting of Global Analysis by Andreas Kriegl and Peter W. Michor, AMS 1997, 618pp
• Hilbert Space Methods for Partial Differential Equations, by R.E. Showalter
• Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, by R. E. Showalter
• Harmonic Analysis and Partial Differential Equations - Björn E.J. Dahlberg and Carlos E. Kenig
• Functional Analysis by Thomas Ward
• Harmonic Function Theory by Sheldon Axler, Paul Bourdon, and Wade Ramey printing disabled
• An Introduction to C*-Algebras by Pierre de la Harpe and Vaughan Jones
• Functional Analysis by Dr. P. G. Dixon
• Introduction to Microlocal Analysis by Richard Melrose

• Fourier Integrals by Victor Palamodov
• Reconstruction of image from projections by Victor Palamodov
• Bernoulli Periodic distributions Notes by Miguel Lerma
• Holomorphic Methods in Analysis and Mathematical Physics by Brian C. Hall

• Nonlinear Analysis and Ordinary Differential Equations by Klaus Schmitt
• Ordinary Differential Equations and Dynamical Systems by Gerald Teschl
• Ordinary Differential Equations Notes by Sheldon Newhouse
• Partial Differential Equations by William W. Symes
• Lectures on analytic differential equations by Yulij Ilyashenko and Sergei Yakovenko
• Exterior Differential Systems and Euler-Lagrange Partial Differential Equations by Robert L. Bryant, Phillip A. Griffiths, Daniel A. Grossman

 

• Introduction to Tensor Calculus and Continuum Mechanics, by John H. Heinbockel
• Topics in Differential Geometry, Peter W. Michor.
• Natural operations in differential geometry by Ivan Kolar, Jan Slovak and Peter W. Michor
• Intrinsic Geometry of Surfaces by A. D. Aleksandrov and V. A. Zalgaller
• An Introduction to Riemannian Geometry - Sigmundur Gudmundsson, Lund University
• Riemann Surfaces, Dynamics and Geometry Curtis McMullen
• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem by Peter B. Gilkey
• Differentiable Manifolds lecture notes (growing) by Mariusz Wodzicki
• Lecture notes for the course in Differential Geometry by Sergei Yakovenko
• Lectures On Symplectic Geometry with and Eye Toward Combinatorics by Sue Tolman
• Differential Geometry lecture notes by Gabriel Lugo
• Differential geometry reconstructed by Alan U. Kennington
• Course of Differential Geometry by Ruslan Sharipov
• A Modern Course on Curves and Surfaces by Richard S. Palais
• Undergraduate notes on Projective Geometry, Manifolds etc. by Nigel Hitchin
• Vector Bundles and an Introduction to Gauge Theory by Steven Bradlow, (Hung-Jen Hsu and Chris Willett)
• Twistor Geometry and Gauge Theory by Martin Wolf
• Complex Geometry of Nature and General Relativity by Giampiero Esposito

• Geometric Asymptotics by Victor Guillemin and Shlomo Sternberg
• Projective Geometry by Balázs Csikós
• Differential Geometry by Balázs Csikós
• Projective and Polar Spaceas by Peter Cameron
• Transformation groups for begginers by S. V. Duzhin and B. D. Tcherbotarevsky

Cartan's Corner Differential geometry & Topology

• Mechanism of the Heavens (1831), by Mary Somerville. This second edition was prepared by Russell McNeil
• Dynamical Systems George D. Birkhoff, AMS 1927, 305 pp.
• Dynamics in One Complex Variable: Introductory Lectures, John Milnor
• Geometrical theory of dynamical systems by Nils Berglun
• Lectures on Mechanics, Dynamics, and Symmetry by Jerrold E. Marsden
• Introduction to Statics and Dynamics by Andy Ruina and Rudra Pratap

• Entropy on the World Wide Web has links to expository articles, journals, software, and conferences pertaining to entropy.
• Dynamical Systems and Ergodic Theory, by Mark Pollicott and Michiko Yuri see also

  Ergodic Theory & Dyn. Sys. for errata and additions.

• Entropy of Compact Group Automorphisms by Thomas Ward
• Valuations and Hyperbolicity in Dynamics by Thomas Ward
• Lecture Notes on Mechanics, Probability and Irreversibility by Alexandre J. Chorin
• Effective Hamiltonians and averaging for Hamiltonian dynamics - Lawrence Craig Evans
   
• Entropy and partial differential equations - Lawrence Craig Evans
   
• CLASSICAL AND QUANTUM CHAOS by Predrag Cvitanovic'

• Schrödinger Operators by Gerald Teschl
• Quantum Mechanics by Klaus Schulten
• lecture notes in Quantum Mechanics by Scott Pratt
• ADVANCED QUANTUM MECHANICS by Jouko Mickelsson
• Foundations of Quantum Mechanics & Quantum Information by M.B. Plenio
• Quantum Geometry and more by Micho Durdevich

• Comprehensive textbook on quantum (and classical) field theory by Warren Siegel
• Quantum Field Theory by Ben Simons
• Mathematical ideas and notions of quantum field theory by Pavel Etingof
• Introduction to Algebraic and Constructive Quantum Field Theory by John C. Baez, Irving E. Segal and Zhengfang Zhou scanned pdf. extermely big 200 megabytes
• Lecture Notes from the Quantum Field Theory program at IAS, 1996-1997
• Books by Warren Siegel
• Introduction to String Theory by Igor V. Dolgachev
• What is String Theory by Joseph Polchinski
• Fluctuating Geometries in Statistical Mechanics and Field Theory Les Houches Session LXII
• Introduction to Superstring Theory by Elias Kiritsis
• Operator Algebras and Quantum Statistical Mechanics, Volumes I & II by Ola Bratteli
• D-Brane Primer by Clifford V. Johnson
• Introduction to Superstring Theory by Elias Kiritsis

• Introduction to Solid-State Physics; Many-Body Theory by Chetan Nayak
• Concepts of Theoretical Solid State Physics by Alexander Altland
• Many-Body Physics by Piers Coleman
• Theory of Superconductivity by Helmut Eschrig
• High-Temperature Superconductivity by Peter Hirschfeld
• Solid State Physics Notes, Problem Sets, & Tests by Peter Hirschfeld
• Complex Surphaces in Materials Science with few books

• Special Relativity on the World Wide Web. Tutorials, lecture notes, and computer simulations.
• Mechanics and Special Relativity introductiry textbook by David Morin
• SERGIU KLAINERMAN General Relativity, Nonlinear PDEs, etc.
• Special Relativity and Geometry by C. E. Harle, R. Bianconi
• Differential Geometry (and Relativity) notes by Bob Gardner
• Lecture Notes on General Relativity by Sean M. Carroll
• General Relativity and Quantum Cosmology by Sean M. Carroll
• Public lectures by Stephen Hawking and Roger Penrose

• Essential Physics 1 by Frank Firk
• Introduction to Groups, Invariants & Particles by Frank W.K. Firk
• Classical Electrodynamics by Bo Thidé
• Classical electrodynamics and theory of relativity by Ruslan Sharipov
• Electromagnetic Theory and Computation: A Topological Approach by Paul W. Gross and P. Robert Kotiuga
• MOTION MOUNTAIN TEXTBOOK Hiking beyond space and time along the concepts of modern physics by Christoph Schiller
• Fundamentals of Thermodynamics by J. Karl Johnson
• Non-Equilibrium Statistical Mechanics by Klaus Schulten
• Course in Electrodynamics by Franz Wegner
• Light and Matter by Ben Crowell
• Order-of-magnitude-physics a book by Sanjoy Mahajan
• A Brief Introduction to Physics for Mathematicians, Igor V. Dolgachev
• Physical Applications of Geometric Algebra by Anthony Lasenby and Chris Doran
• Group Theory for Physicists by Predrag Cvitanovic'
• An Elementary Introduction to Groups and Representations by Brian C. Hall
• Geometric Models for Noncommutative Algebras by A. Cannas da Silva and A. Weinstein
• Teaching electromagnetic field theory using differential forms by K.Warnick,R.Selfridge and D.Arnold
• Lectures on integration of several variables by Michael Adler
• Methods of Mathematical Physics by Mark Trodden
• Concepts in Theoretical Physics by Ben Simons
• Further Mathematical Methods by Niels Walet
• Computational Physics by Angus MacKinnon

 

• Numerical Analysis Notes by Lucio Tavernini
• An Introduction to Multigrid Methods by Pieter Wesseling
• Finite Element Method/Boundry Element Method by Peter Hunter
• Numerical Recipes by William H.Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery
• Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods by Barrett, Richard
• Numerical Analysis at the University of Cambridge
• Numerical Mathematics and Scientific Computation by Germund Dahlquist and Åke Björck

• Lecture Notes on Optimization by Pravin Varaiya
• Computational geometry, mesh generation, numerical methods by Jonathan Shewchuk
• Numerical Analysis by Steven Elliot Pav

• Information Theory, Inference and Learning Algorithms. A Textbook by David J.C. MacKay
• A Short Course in Information Theory - 8 lectures by David J.C. MacKay
• Primer on Information Theory by Thomas Schneider
• Several books ! by G. J. Chaitin (not only Information Theory)

• Applied Quantitative Finance by W. Härdle, T. Kleinow, G. Stahl printing disabled
  Also other non-printable books on the same page
• Measure theory, Probability, Stochastic calculus, General theory of processes, Financial mathematics lectures notes by Rich Bass
• Lectures on Stochastic Calculus and Finance by Steven Shreve
• Structural Analysis of Discrete Data and Econometric Applications, editors: Ch. Manski, D. McFadden
• Handbook of Econometrics, editiors: J. J. Heckman, E. Leamer and R. Blundell
• Essential Principles of Economics by Roger McCain
• Game theory examples by Roger McCain (html)

• Gametheory.net with lectures on the subject
• Determinacy in infinite games by Jindrich Zapletal

• Handbook of Applied Cryptography, by Alfred J. Menezes , Paul C. van Oorschot, and Scott A. Vanstone
• Foundations of Cryptography
• Lecture Notes on Cryptography
• Cryptography and Network Security
• Cryptography and Cryptanalysis Lecture notes
• Modern Cryptography
• Cryptography and Cryptanalysis by Glenn Durfee
• Lecture Notes on Cryptography by S. Goldwasser and M. Bellare

• Introduction to Statistical Signal Processing by R.M. Gray and L.D. Davisson

• Fractals in the Plane - the Ergodic Theory Methods by F. Przytycki and M. Urbanski
• Lecture notes in Conformal Dynamics, taught by Curt McMullen.
• Fractals by Dr. P. G. Dixon

• Graph Theory with Applications by J.A. Bondy and U.S.R. Murty
• Graph Theory by Reinhard Diestel printing disabled
• Interactive Graph theory tutorials by Chris K. Caldwell must register to use

• Mirrors and Reflections: The Geometry of Finite Reflection Groups by Alexandre V. Borovik, Anna s. Borovik
• Miscellaneous facts about Coxeter groups by Robert B. Howlett
• Buildings, BN-pairs, Hecke algebras, classical groups by Paul Garrett

• Ross Geoghegan's Home Page has a set of papers

• Mathematics of Rubik's cube by David Joyner is a good source for discrete group theory with applications to permutation puzzles.

How to prepare documents? TEX,LATEX etc.

• Formatting information - A beginner's introduction to typesetting with LaTeX by Peter Flynn
• TeX by Topic the TeXbook of Victor Eijkhout
• LaTeX2e for authors
• Mathematical Illustrations, a manual of geometry and postscript by Bill Casselman

• The TeXbook by Donald Knuth is the most comrehensive book about TEX (tex source)
• The METAFONTbook is also downloadable (tex source)
  The last two books are copyrighted and you are not supposed to compile them. These files are, in fact, much more than sources of textbooks. They are invaluable examples of TeX input.

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