Mathematical Methods of Engineering Analysis

Book by Erhan Çinlar and Robert J. Vanderbei in PDF. Topics covered: functions on metric spaces, differential and integral equations, convex analysis, and measure and integration.
http://www.sor.princeton.edu/~rvdb/506book/book.pdf

Wavelets

An Introduction to Wavelets by Amara Graps in HTML, PDF or Postscript.
http://www.amara.com/IEEEwave/IEEEwavelet.html

Probability

"Introduction to Probability" by Charles M. Grinstead and J. Laurie Snell in PDF. Published by the AMS. The site also contains additional teaching resources.
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html

Multivariable Calculus

Textbook by George Cain and James Herod. Chapters in PDF.
http://www.math.gatech.edu/~cain/notes/calculus.html

History of Calculus

Guide To History of Calculus. Topic essays and biographies keyed to the chapters and content of the 10th edition of Thomas's Calculus.
http://occ.awlonline.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/deluxe-content.html

Algebraic Geometry

Various lecture notes by J.S. Milne.
http://www.jmilne.org/math/

Linear Methods of Applied Mathematics

Textbook suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations by Evans M. Harrell II and James V. Herod. HTML, RTF and PDF with Maple and Mathematica worksheets.
http://www.mathphysics.com/pde/

Algebraic Topology

Basic core material along with a number of optional topics of a relatively elementary nature by Allen Hatcher. PDF and Postscript.
http://www.math.cornell.edu/~hatcher/

Numerical Recipes Books On-Line

The complete Numerical Recipes books in C, Fortran 77, and Fortran 90 On-Line, in both PostScript and Adobe Acrobat formats.
http://www.nr.com/nronline_switcher.html

Mixed Motives

Monograph by Marc Levine published by AMS in 1998. Whole book or chapters in PDF.
http://www.ams.org/online_bks/surv57/surv57.pdf

Tensor Calculus and Continuum Mechanics

Textbook by John H. Heinbockel. Whole book or chapters in PostScript and PDF.
http://www.math.odu.edu/~jhh/counter2.html

C*-Algebras

"An Introduction to C*-Algebras" by Pierre de la Harpe and Vaughan Jones. The site is in French, but the book is in English. Chapters in PostScript.
http://www.unige.ch/math/biblio/preprint/cstar/liste.html

Abstract Algebra II

A companion volume to "Abstract Algebra" by John A. Beachy and Bill Blair published by Waveland Press in 1995. Chapters in PostScript.
http://www.math.niu.edu/~beachy/abstract_algebraII/

Advanced Calculus and Analysis

Lecture notes by Ian Craw from a course at the Univ. of Aberdeen. HTML with GIFs.
http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/notes.html

Complex analytic and algebraic geometry

Book by Jean-Pierre Demailly in PostScript.
http://www-fourier.ujf-grenoble.fr/~demailly/books.html

Linear Algebra and Applications

Textbook by Thomas Shores. GIFs of pages.
http://www.math.unl.edu/~tshores/linalgtext.html

Mathematical Principles of Natural Philosophy

Principia by Isaac Newton (1687) translated by Andrew Motte (1729) in HTML (incomplete).
http://members.tripod.com/~gravitee/

Plane Geometry

Shalosh B. Ekhad XIV. A fully illustrated and completely self-contained Elementary Geometry textbook (ca. 2050), downloaded from the future by Doron Zeilberger. Entirely written in Maple.
http://www.math.rutgers.edu/~zeilberg/GT.html

Numerics - interactive

In this PDF book by Thomas Risse, basic numerical algorithms are presented and implemented in order to determine the precision of computation, to solve systems of linear equations, to evaluate elementary functions, to find zeros, to integrate and to solve
http://www.weblearn.hs-bremen.de/risse/MAI/docs/numerics.pdf

Graph Theory

Hyperlinked PDF version of a book by Reinhard Diestel.
http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/download.html

Stochastic Calculus

A fairly complete elementary introduction to the basics of stochastic integration with respect to continuous semimartingales by Alan Bain. All the theory usually needed for basic mathematical finance. Sixty pages in dvi, postscript, and pdf.
http://www.statslab.cam.ac.uk/~afrb2/

Linear Algebra

"Elementary Linear Algebra" by Keith Matthews. Lecture notes and solutions from 1991 in PDF or PostScript.
http://www.numbertheory.org/book/

Dynamical Systems and Ergodic Theory

"Lectures on Dynamical Systems and Ergodic Theory" by Mark Pollicott and Michiko Yuri. Published by Cambridge University Press in 1998 (London Mathematical Society Students Texts, No. 40).
http://www.ma.man.ac.uk/~mp/book.html

Optimization

"Lecture Notes on Optimization" by Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming.
http://www-path.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf

Abstract Algebra

Course notes by J.S. Milne. Topics covered are group, fields and Galois, algebraic number, class field theories. Other areas discussed are modular functions and forms, elliptic curves, algebraic geometry, Etale Cohomology, and Abelian varieties. In HTML
http://www.jmilne.org/math/CourseNotes/

Differential Geometry

Lecture notes for a course at the Weizmann Institute of Science by Sergei Yakovenko. Chapters in DVI.
http://www.wisdom.weizmann.ac.il/~yakov/Geometry/

Generatingfunctionology

By Herbert S. Wilf. Published by Academic Press. PDF.
http://www.math.upenn.edu/~wilf/DownldGF.html

Euclid's Elements

Edited by D.E. Joyce. HTML text with Java applets.
http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

Fundamentals of Model Theory

Introductory textbook by William Weiss and Cherie D'Mello. PostScript, DVI, GIF.
http://at.yorku.ca/i/a/a/i/10.htm

A=B

Combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters. PDF.
http://www.cis.upenn.edu/~wilf/AeqB.html

Abstract Algebra

Three books by Robert B. Ash (chapters in PDF): Abstract Algebra: The Basic Graduate Year, A Course In Algebraic Number Theory, and A Course In Commutative Algebra.
http://www.math.uiuc.edu/~r-ash/

Practical Foundations of Mathematics

An account of the foundations of mathematics (algebra) and theoretical computer science, from a modern constructive viewpoint by Paul Taylor. Published by Cambridge University Press. HTML approximation.
http://www.dcs.qmw.ac.uk/~pt/Practical_Foundations/html/summary.html

Elements of Abstract and Linear Algebra

Foundational textbook on abstract algebra with emphasis on linear algebra by Edwin H. Connell. Whole book or chapters in DVI, PostScript, and PDF.
http://www.math.miami.edu/~ec/book/

Complex Analysis

Textbook for an introductory course in complex analysis by George Cain. Chapters in PDF.
http://www.math.gatech.edu/~cain/winter99/complex.html

Universal Algebra

"A Course in Universal Algebra" by Stanley Burris and H. P. Sankappanavar. PostScript and PDF.
http://www.thoralf.uwaterloo.ca/htdocs/ualg.html

Index Theory, Geometric Scattering, and Differential analysis on manifolds with corners

Several books by Richard Melrose et al. in PostScript.
http://www-math.mit.edu/~rbm/book.html

Linear Algebra

Textbook by Jim Hefferon covering the material of any undergraduate first linear algebra course. Book or chapters in PDF.
http://joshua.smcvt.edu/linalg.html

Abstract Algebra

Lecture notes by David Wilkins at Trinity College, Dublin.
http://www.maths.tcd.ie/~dwilkins/Courses/311/

Templates for the Solution of Linear Systems

Book on iterative methods by Richard Barrett et al. in HTML and Postscript.
http://netlib2.cs.utk.edu/linalg/html_templates/Templates.html

Semi-Simple Lie Algebras and their Representations

Book for particle physicists by Robert N. Cahn. Published by Benjamin-Cummings in 1984. Chapters in PostScript.
http://www-physics.lbl.gov/~rncahn/book.html

Linearization via the Lie Derivative

By Carmen Chicone and Richard Swanson. LaTeX, DVI, PostScript and PDF.
http://ejde.math.swt.edu/Monographs/02/abstr.html

Finite Rank Torsion Free Modules Over Dedekind Domains

Monograph in commutative ring theory by Lee Lady. DVI and PDF.
http://www.math.hawaii.edu/~lee/book/

Topology Course Lecture Notes

By Aisling McCluskey and Brian McMaster. HTML with symbol fonts, DVI and PostScript.
http://at.yorku.ca/i/a/a/b/23.htm

Trigonometry

"Dave's Short Trig Course" by D. E. Joyce. HTML with Java.
http://aleph0.clarku.edu/~djoyce/java/trig/

Analysis WebNotes

Online course by John Lindsay Orr. Chapters also available in LaTeX.
http://www.math.unl.edu/~webnotes/home/home.htm

Interactive Real Analysis

"Interactive Real Analysis" by Bert G. Wachsmuth. HTML and Java.
http://www.shu.edu/html/teaching/math/reals/reals.html

Complex and Functional Analysis

Lecture notes by Douglas N. Arnold for a course at Penn State. Two parts in TeX, DVI, PostScript and PDF.
http://www.math.psu.edu/dna/502.s97/

Category Theory

"A Gentle Introduction to Category Theory - the calculational approach" by Maarten M. Fokkinga in PostScript.
http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html

Multiplier Ideals for Algebraic Geometers

Draft of a part of a book in preparation on positivity in algebraic geometry by Robert Lazarsfeld. DVI and PostScript.
http://www.math.lsa.umich.edu/~rlaz/

Dynamical Systems

1927 classic by George D. Birkhoff published by AMS. Scanned chapters in PDF.
http://www.ams.org/online_bks/coll9/

Physics, Invariant Theory, Modular Forms, and Algebraic Geometry

Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript.
http://www.math.lsa.umich.edu/~idolga/lecturenotes.html

Differential Geometry

Notes by Balázs Csikós. Chapters in PostScript.
http://www.cs.elte.hu/geometry/csikos/dif/dif.html

Functional Analysis and Semi-Groups

Book by Einar Hille and Ralph S. Phillips published by AMS in 1957. Scanned chapters in PDF.
http://www.ams.org/online_bks/coll31/

Global Analysis

"The Convenient Setting of Global Analysis" - foundations of differential calculus in infinite dimensions with applications to differential geometry and global analysis by Andreas Kriegl and Peter W. Michor published by AMS in 1997. Whole book or chapter
http://www.ams.org/online_bks/surv53/

Complex Dynamics in Higher Dimensions

CBMS lecture notes by John Erik Fornæss at the bottom of page with other papers by the author and Nessim Sibony. PostScript.
http://www.math.lsa.umich.edu/~fornaess/complexdynamicspapers.html

Several complex variables

Several sets of lecture notes by Jean-Pierre Demailly, some in French, including "Potential theory in several complex variables", and "Multiplier ideal sheaves and analytic methods in algebraic geometry" in DVI or PostScript.
http://www-fourier.ujf-grenoble.fr/~demailly/lectures.html

Algebraic Topology

1942 classic by Solomon Lefschetz published by AMS. Chapters in scanned PDF.
http://www.ams.org/online_bks/coll27/

Travelling Wave Solutions of Parabolic Systems

Translation of a monograph by Aizik Volpert, Vitaly Volpert, and Vladimir Volpert published by AMS in 1994. Whole book or chapters in PDF.
http://www.ams.org/online_bks/mmono140/

Differential Geometry

Several books by Peter W. Michor et al. including "Foundations of Differential Geometry", "Natural operations in differential geometry" (corrected version), "Transformation Groups", and "Gauge theory for fiber bundles" plus papers by the author in postscr
http://www.mat.univie.ac.at/~michor/listpubl.html

Computational Geometry and Computational Optimization

Lecture notes by Jianer Chen in PostScript.
http://www.cs.tamu.edu/faculty/chen/notes/

Differential Topology

Course notes by Matthew G. Brin in PostScript including "Introduction to Differential Topology", "Introduction to Seifert fibered 3-manifolds", "Groups acting on 1-dimensional spaces", and "Presentations, conjugacy, roots and centralizers in groups of pi
http://www.math.binghamton.edu/matt/

Linear Programming: Foundations and Extensions

Book by Robert J. Vanderbei in PDF.
http://www.princeton.edu/~rvdb/LPbook/

Numerical Analysis

"Introduction to Numerical Analysis Using Maple" by Barry G. Adams in HTML.
http://www.cs.laurentian.ca/badams/numeric/intro/intro.html

Dynamical Systems and Fractals

Lecture Notes by David J. Wright in HTML.
http://www.math.okstate.edu/mathdept/dynamics/lecnotes/lecnotes.html

Mathematical Modeling in a Real and Complex World

Online guide book by Frank Wattenberg in HTML.
http://www.math.montana.edu/frankw/ccp/modeling/topic.htm

Geometric Constraint Solving

An electronic primer by William Bouma, Xiangping Chen, Ioannis Fudos, Christoph Hoffmann, and Pamela J. Vermeer.
http://www.cs.purdue.edu:80/homes/cmh/electrobook/intro.html

Fundamental Problems in Algorithmic Algebra

Book by Chee Yap published by Oxford University Press in 1999.
http://www.cs.nyu.edu/yap/book/

Abstract Algebra

"Intro to Abstract Algebra" by Paul Garrett in PostScript and PDF.
http://www.math.umn.edu/~garrett/m/intro_algebra/

The FEMCI Book

Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.
http://analyst.gsfc.nasa.gov/FEMCI/femcibook.html

Algebraic K-theory

"An introduction to algebraic K-theory" by Charles Weibel. Chapters in DVI.
http://math.rutgers.edu/~weibel/Kbook.html

Complex Analysis

Course notes by Harold V. McIntosh in HTML.
http://delta.cs.cinvestav.mx/~mcintosh/comun/complex/complex.html

Dynamics in One Complex Variable: Introductory Lectures

Lecture notes by John Milnor in TeX and PostScript.
http://www.math.sunysb.edu/cgi-bin/preprint.pl?ims90-5

The Limits of Mathematics

An online course on information theory and the limits of formal reasoning by G.J. Chaitin.
http://www.umcs.maine.edu/~chaitin/lm.html

Hilbert Space Methods for Partial Differential Equations

Textbook for beginning graduate students of mathematics, engineering, and the physical sciences by Ralph Showalter. Chapters in PostScript and PDF.
http://ejde.math.swt.edu/Monographs/01/abstr.html

Differential Gometry and General Relativity

An introduction to differential geometry and general relativity by Stefan Waner at Hofstra. This is an upper level undergraduate mathematics course which assumes a knowledge of calculus and some linear algebra.
http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html

Algebraic Combinatorics via Finite Group Actions

HTML book by A. Betten, H. Fripertinger, and A. Kerber.
http://www.mathe2.uni-bayreuth.de/frib/html/book/hyl00.html

Basic Concepts of Mathematics

This text by Elias Zakon helps the student complete the transition from purely manipulative to rigorous mathematics. Chapters cover Set Theory, the Real Numbers, and n-dimensional Geometry.
http://www.trillia.com/zakon1.html

Geometric Asymptotics

This book by Guillemin and Sternberg includes the method of stationary phase, geometrical optics, quantization.
http://www.ams.org/online_bks/surv14/

Differential Algebra

Scans of Ritt's 1950 classic in PDF.
http://www.ams.org/online_bks/coll33/

Applied Cryptography

1996 CRC Handbook of Applied Cryptography by Menezes, van Oorschot and Vanstone in PDF.
http://cacr.math.uwaterloo.ca/hac/

Linear Algebra, Infinite Dimensions, and Maple

A textbook by James Herod.
http://www.math.gatech.edu/~herod/Hspace/Hspace.html

Homeomorphisms in Analysis

A survey by C. Goffman, T. Nishiura, D. Waterman in PDF. In particular, the effects of homeomorphic changes of domain on the analyticity of a function are studied.
http://www.ams.org/online_bks/surv54/

Finite Simple Groups

"The classification of the finite simple groups" by D. Gorenstein, R. Lyons, and R. Solomon in PDF.
http://www.ams.org/online_bks/surv40-1/

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations

A monograph by Ralph Showalter in PDF.
http://www.ams.org/online_bks/surv49/

Matrices

The 1934 classic "Lectures on Matrices" by Wedderburn in scanned PDF.
http://www.ams.org/online_bks/coll17/

Algebraic Geometry

A. Grothendieck's "Séminaire de Géometrie Algébrique" produced by F. Calegari, J. Borger and W. Stein. JPEG scans of typewritten material.
http://modular.fas.harvard.edu/sga/sga/

Numerical Grid Generation

A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML.
http://www.erc.msstate.edu/publications/gridbook/

Toposes, Triples and Theories

A book by Michael Barr and Charles Wells originally published by Springer Verlag.
http://www.cwru.edu/artsci/math/wells/pub/ttt.html

Multigrid Methods

"An Introduction to Multigrid Methods" by Pieter Wesseling.
http://www.mgnet.org/mgnet-books-wesseling.html

Calculus

"The Calculus Bible" by G. S. Gill.
http://www.math.byu.edu/Math/CalculusBible/

Dynamics and Chaos

Class notes by Evans M. Harrell II for an introductory course on dynamical systems and chaos, taken by mathematicians, engineers, and physicists. This text concentrates on models rather than proofs in order to bring out the concepts of dynamics and chaos
http://www.mathphysics.com/dynam/

Entropy of Compact Group Automorphisms

Lecture notes based on a course at Ohio State in 1994 by Thomas Ward in DVI and PostScript.
http://www.mth.uea.ac.uk/~h720/lecture_notes/

Complex-Analytic Geometry of Complex Parallelizable Manifolds

Monograph by Jörg Winkelmann. Chapters in DVI.
http://www.math.unibas.ch/~winkel/cplx/papers/gca.html

Finite Applied Associative Algebra (semigroups) & Digital Networks

A compendium of papers by Nico F. Benschop on abstract algebra, number theory, computer science and physics.
http://home.iae.nl/users/benschop

Matrix Analysis and Applied Linear Algebra

By Carl D. Meyer. Full text in PDF with errata, updates and solutions.
http://www.matrixanalysis.com/

Complex Numbers

Dave's Short Course on Complex Numbers (David Joyce).
http://www.clarku.edu/~djoyce/complex/

Discrete Mathematics

Lecture notes by László Lovász in Postscript. Includes "Discrete Mathematics", "Semidefinite optimization", "Topological methods in combinatorics", and "Complexity of algorithms".
http://research.microsoft.com/users/lovasz/notes.htm

Topology

"Textbook in Problems on Elementary Topology" by Viro, Ivanov, Kharlamov and Netsvetaev - draft version in postscript. The page also includes several papers on real algebraic geometry.
http://www.math.uu.se/~oleg/educ-texts.html

Splines and Wavelets

A monograph by Karl Scherer in German (DVI and Postscript).
http://www.iam.uni-bonn.de/~scherer/wavelets.html