You might wish to consult also other lists and collections
 

Free, online MATHEMATICS BOOKS

• Project Gutenberg math section contains many open access books.
• European Mathematical Information Service (EMIS). Lots of monographs and lecture notes.
• Czech Digital Mathematics Library offers open access to many single books and/ collections ...
  Many are in English, but just as many are in Czech.
• A New Kind of Science by Stephen Wolfram (first printed in 2002).
  Software, math and physics. Page-by-page access.
• A = B, book about combinatorial identities by Marko Petkovsek, Herbert S. Wilf and Doron Zeilberger.
• A Computational Introduction to Number Theory and Algebra by Victor Shoup.
• Abelian Categories by Peter Freyd.
• Abstract and concrete categories: The joy of cats
  by Jiri Adamek, Horst Herrlich and George Strecker. Alternative source.
• Advanced Calculus by Lynn Loomis and Shlomo Sternberg.
• Algebraic Topology, Vol.I, by Allen Hatcher. Available also in printed form.
• Algorithms and Complexity, 1st Edition, by Herbert S. Wilf. You can buy the 2nd Edition.
• Arithmetic Duality Theorems by James S.Milne. Available also in printed form.
• Asynchroneous Systems Theory by Serban E.Vlad. Published by WSEAS.
• Automorphic Forms, Shimura Varieties, and L-functions, Volumes I and II.
  Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 6-16, 1988.
  Edited by L.Clozel and James S.Milne.
• Basic Concepts of Enriched Category Theory by Max Kelly.
• Basic Concepts of Mathematics by Elias Zakon, courtesy of the Trillia Group.
• Basics of Algebra and Analysis for Computer Science by Jean Gallier.
• Categories and Groupoids by late Philip J.Higgins.
• Chaos: Classical and Quantum by Predrag Cvitanovic'.
• Combinatorial and Computational Geometry, a 2005 collection of articles edited by
  Jacob E. Goodman, János Pach and Emo Welzl. Available also in printed form
• Complex Variables by Robert B. Ash and Phil Novinger.
• Complex Analysis by George Cain.
• Concepts and Applications of Inferential Statistics by Richard Lowry. Click Table of Contents.
• Concise Encyclopedia of Mathematics by Eric Weisstein.
  1998 version available also in printed form and on CD.
• Convex Optimization by Stephen P. Boyd and Lieven Vandenberghe.
  Available also in printed form. Original Edition Cambridge University Press 2004.
• Difference Equations to Differential Equations by Dan Sloughter.
• Dynamical Systems by Shlomo Sternberg.
• Dynamics in One Complex Variable by John Milnor.
  1st Edition, IMS 1990. Also available: Printed 3rd Edition.
• Dynamics, Ergodic Theory, and Geometry, a 2007 collection of articles
  edited by Boris Hasselblatt. Available also in printed form
• E Infinity Ring Spectra and E Infinity Ring Spaces by J. Peter May et al
  (Springer 1977). Available also in printed form.
• Elementary Calculus: An Approach Using Infinitesimals by H.J.Keisler.
• Elements of Abstract and Linear Algebra by Edwin H. Connell.
• Elliptic Curves by James S. Milne. Available also in printed form.
• Entropy and Information Theory by Robert M. Gray.
• Euclid's Elements edited by David E. Joyce.
• Equivariant Stable Homotopy Theory by L. G. Lewis Jr, J. Peter May, M. Steinberger, J. E. McClure.
  Available also in printed form.
• Finite Element Methods by Nikos Mastorakis and Olga Martin. Published by WSEAS.
• Foundations of Combinatorics with Applications by Edward A. Bender and Gill S. Williamson
• Foundations of Differentiable Manifolds and Lie Groups by Frank W. Warner.
  DjVu format. Available also in printed form.
• Generatingfunctionology, 2nd Ed., by Herbert S. Wilf, and the publisher, A.K.Peters.
• Geometric Asymptotics by Shlomo Sternberg, on AMS Online
• Graph Algorithms by the late Shimon Evan (Chapters 1-6, .ps format). more >>.
• Graph Theory by Reinhard Diestel. Not really free. Available also in printed form.
• Group Theory: Birdtracks, Lie’s, and Exceptional Groups by Predrag Cvitanovic'.
• H Infinity Ring Spectra and their Applications by R. R. Brunner, J. Peter May,
  J. E. McClure, M. Steinberger (Springer 1986). Available also in printed form.
• Handbook of Mathematical Functions edited by M. Abramowitz and A. Stegun.
• Hodge Cycles, Motives, and Shimura Varieties by Pierre Deligne,
  James S.Milne, Arthur Ogus and Kuang-yen Shih. Available also in printed form.
• Information Theory, Inference, and Learning Algorithms, by David MacKay. Available also in print.
• Introduction to Bayesian Statistics by H.Thornburg.
• Introduction to Matrix Algebra by Autar Kaw.
• Introduction to Probability Theory by Charles M. Grinstead and J. Laurie Snell.
  GNU License. Acompanied by a number of tools and links. Available also in printed form.
• Introduction to Probability and Random Processes by Gian-Carlo Rota and Kenneth P. Baclawski.
• Introduction to Real Analysis by William Trench. PDF shortcut and an alternative.
• Introduction to Statistical Data Processing by Robert M. Gray and L. D. Davisson.
  Courtesy Cambridge University Press. Available also in printed form.
• Introduction to the Theory of Numbers by Leo Moser, courtesy of Trillia Group.
• Introduction to Vectors and Tensors by Ray M. Bowen and C. C. Wang.
  Vol.1: Linear and Multilinear Algebra and Vol.2: Vector and Tensor Analysis
• Inverse Problem Theory and Methods for Model Parameter Estimation
  by Albert Tarantola, SIAM 2005. Available also in printed form.
• Jacobi Operators and Completely Integrable Nonlinear Lattices by Gerald Teschl.
  Available also in printed form.
• Lie Algebras by Shlomo Sternberg.
• Linear Algebra, a free text for a standard US undergraduate course, by Jim Hefferon.
• Linear Algebra, Infinite Dimensions, and Maple, an online book by Jim Herod.
• Linear Controller Design - Limits of Performance
  by Stephen Boyd and Craig Barratt. Original Edition Prentice Hall 1991.
• Linear Matrix Inequalities in System and Control Theory
  by Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Ragu Balakrishnan.
  Available also in printed form. Original Edition SIAM 1997.
• Linear Methods of Applied Mathematics by E.M.Harrell II and J.Herod.
• Linear Partial Differential Equations and Fourier Theory (online version) by Marcus Pivato.
• Logic for Computer Science: Foundations of Automatic Theorem Proving
  by Jean Gallier. Not sure whether it is really downloadable.
• Manuscripts of Srinivasa Ramanujan at Tata Institute of Fundamental Research. 3 volumes.
• Mapping of Probabilities - Theory for the Interpretation of Uncertain Physical Measurements, an online book by the late Albert Tarantola. In preparation; only first two Chapters are finished.
• Mathematical Analysis I by Elias Zakon, courtesy of the Trillia Group.
• Mathematical Analysis II by Elias Zakon, courtesy of the Trillia Group.
• Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications, J. O. Smith III.
• Multivariable Calculus by George Cain and James Herod.
• My Algebra Book by Eric Kean. A nice college algebra initiative.
• NIST Digital Library of Mathematical Functions,
  a vastly enlarged continuation of the Abramowitz-Stegun Handbook.
• Notes on Convex sets, Polytopes, Polyhedra, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations by Jean Gallier.
• Notes on Differential Geometry by Noel J. Hicks (1965).
• Notes on Differential Geometry and Lie Groups
  by Jean Gallier and Jocelyn Quaintance.
• Number Theory, an undergraduate revision by Jim Hefferon of a text by W. E. Clark.
• Practical Foundations of Mathematics by Paul Taylor. Available also in printed form
• Predicative Arithmetic by Edward Nelson.
• Probability, geometry, and integrable systems, a 2008 collection of articles
  edited by Mark Pinsky and Björn Birnir. Available also in printed form
• Probability Theory: The Logic of Science by Edwin T. Jaynes.
• Probability, Random Processes, and Ergodic Properties by R.M.Gray.
• Radically Elementary Probability Theory by Edward Nelson.
• Real Variables with Basic Metric Space Topology by Robert B. Ash.
  Originally published by IEEE Press in 1992. 78 MB pdf.
• Rough Set Data Analysis: A road to non-invasive knowledge discovery,
  a primer by Ivo Düntsch and Günther Gediga. Available also in printed form
• Semiriemannian Geometry by Shlomo Sternberg.
• Sequential Simplex Optimization (PDF 3.8 Mb) by Walters F.H., Morgan S.L., Parker L.R.Jr., Deming S.N., CRC Press 1991. Licensed electronic reprint 1999.
• Semi-classical Analysis by Shlomo Sternberg.
• Seminar on Triples and Categorical Homology Theory,
  edited by Beno Eckmann and Myles Tierney.
• Sets, Relations, Functions, a primer by Ivo Düntsch and Günther Gediga. More >>.
• Simple Groups of Finite Morley Rank
  by Tuna Altinel, Alexandre V. Borovik, and Gregory Cherlin. Early version on AMS.
• Spectral Sequences in Algebraic Topology by Allen Hatcher.
• Statistics: Methods and Applications by Thomas Hill and Paul Lewicki at StatSoft.
  Available also in printed form.
• StatLect - Lectures on Probability and Statistics by Marco Taboga. Very good.
• Tensor Analysis by Edward Nelson.
• The Calculus of Functions of Several Variables by Dan Sloughter.
• The Geometry of Iterated Loop Spaces by J. Peter May.
• The Homology of Iterated Loop Spaces by Frederick R. Cohen, Thomas J. Lada and J. Peter May. Available also in printed form.
• Theory of Functions of a Real Variable by Shlomo Sternberg.
• Toeplitz and Circulant Matrices: A Review by R.M.Gray. Available also in printed form.
• Toposes, Triples and Theories by Michael Barr and Charles Wells.
• Trigonometric Delights by Eli Maor. Limited online availability.
• Understanding Calculus by F. Hussain. Very good.
• Vector Bundles and K-Theory by Allen Hatcher.
• Wavelets - all there is to know about them. Do not miss this resource!
• Wolfram MathWorld. The web's most extensive mathematics resource.

Free, online books and similar resources RELATED to MATHEMATICS

• The Online Encyclopedia of Integer Sequences, OEIS (ex Sloane's).
  This is not really a book, but it counts as one. There is also a Wiki
• A Treatise on Probability: The Connection Between Philosophy and the History of Science
  by John M.Keynes. Available also in printed form
• Assessing Mathematical Proficiency, a 2007 collection of articles
  edited by Alan H.Schoenfeld. Available also in printed form
• Design of Comparative Experiments by Rosemary A.Bailey.
  Available also in printed form. Original Edition Cambridge University Press 2008.
• Entropy and Information Theory by R.M.Gray.
  Could be available also in printed form.
• Maths from Scratch for Biologists by Allan J.Cann.
  Available also in printed form.
• Mathematical Illustrations by Bill Casselman.
• Mathematical Tools for Physics by James Nearing.
• Mathematics for Algorithm and Systems Analysis
  by Edward A. Bender and Gill S. Williamson.
• Mathematics of Climate Change from MSRI.
• Numerical Methods and Analysis for Engineers by Douglas W.Harder.

Free, online Math Courses, Lecture Notes and Textbooks

• Lectures on Mathematics at Tata Institute of Fundamental Research. 92 titles and growing.
• A Concise Course in Algebraic Topology by J. Peter May. Available also in dvi and printed form.
• A First Course in Linear Algebra (FCLA), a textbook by Rob Beezer. Excellent.
• A Primer of Real Analysis, an online textbook by Dan Sloughter.
• A Problem Text in Advanced Calculus by John M.Erdman.
• A Short Course in Discrete Mathematics by Edward A. Bender and Gill S. Williamson.
• Abstract Algebra: The Basic Graduate Year, a textbook by Robert B.Ash.
• Abstract Algebra: Theory and Applications, 2009 college textbook by Thomas W.Judson.
• Algebraic Number Theory, a course by Robert B. Ash.
• An Introduction to Set Theory, an almost complete course/textbook
  by William Weiss. PDF / PS / DVI formats.
• Analysis of Functions of a Single Variable, a textbook by Lawrence Baggett.
• Basic Analysis: Introduction to Real Analysis, a nice textbook by Jiri Lebl.
• Calculus, a textbook by B.Crowell.
• Calculus, a textbook by Gilbert Strang at MIT Open Courseware.
• Commutative Algebra, a course by Robert B. Ash.
• Complex Analysis interactive textbook by Bert G.Wachsmuth.
• Elementary Linear Algebra, lecture Notes by Keith Matthews.
• Functional Analysis, an online textbook by Lawrence Baggett.
• Fundamentals of Model Theory, a course/textbook
  by William Weiss and Cherie D'Mello. PS / DVI / AtlasImage formats.
• Group Theory course by James S.Milne.
• HyperStat Online Statistics Textbook by David M.Lane. Great resource.
• Lectures on Statistics by Robert B. Ash.
• Lectures Notes on Optimization by Pravin Varaiya.
  Online PDF re-issue of a book out of print since 1975.
• Lectures on Analytic Differential Equations
  by Yulij Ilyashenko and Sergei Yakovenko. Available also in printed form.
• Lectures on Modular Functions of One Complex Variable by Hans Maass.
• Math Alive, lecture Units by Ingrid Daubechies and Shannon Hughes.
• Modern Course on Curves and Surfaces, lecture notes by R.Palais.
• Modular Functions and Modular Forms (Elliptic Modular Curves) by James S.Milne.
• Notes on Differential Equations, lecture notes by Bob Terrell.
• Notes on Diffy QS: Differential Equations for Engineers, a nice textbook by Jiri Lebl.
• Ordinary Differential Equations and Dynamical Systems, a textbook by Gerald Teschl.
• Real Analysis interactive textbook by Bert G.Wachsmuth.
• Topology Course Lecture Notes by Aisling McCluskey and Brian McMaster.
• Yet Another Calculus Text: A short introduction with infinitesimals,
  a textbook by Dan Sloughter.

Free, online MATHEMATICAL THESES

• 1994 J. D. Howroyd, PhD, University of London,
  On the theory of Hausdorff measures in metric spaces.
• 1960 Edward A.Flinn III, PhD, Caltech,
  Exact Transient Solution of Some Problems of Elastic Wave Propagation.