Books

Here’s a list of ebooks / lecture notes on various fields of Mathematics, Physics, Electrical Engineering, Computer Science, Economics, etc.

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Algebraic Geometry:

• Algebraic Curves [pdf]
  William Fulton

• Algebraic Geometry [pdf]
  Alexei Skorobogatov

• Current Topics in Complex Algebraic Geometry
  Herbert Clemens, János Kollár (editors)

• Topics in Classical Algebraic Geometry [pdf]
  Igor V. Dolgachev

Algebraic Topology:

• A Concise Course in Algebraic Topology [pdf]
  J.P. May

• Algebraic Topology
  Allen Hatcher

Algorithms & Complexity:

• Algorithms
  Sanjoy Dasgupta, Christos Papadimitriou, Umesh Vazirani

• Algorithms and Complexity
  Herbert Wilf

• Combinatorial Algorithms
  Albert Nijenhuis, Herbert Wilf

• Computational Complexity: a Modern Approach
  Sanjeev Arora, Boaz Barak

• The Design of Approximation Algorithms
  David P. Williamson, David B. Shmoys

Calculus:

• Calculus
  Gilbert Strang

• Elementary Calculus: An Infinitesimal Approach
  H. Jerome Keisler

• Multivariable Calculus
  George Cain, James Herod

Computer Arithmetic:

• Modern Computer Arithmetic
  Richard Brent, Paul Zimmermann

Control Theory:

• Adaptive Control: Stability, Convergence, and Robustness
  Shankar Sastry, Marc Bodson

• A Mathematical Approach to Classical Control
  Andrew D. Lewis

• An Introduction to Mathematical Optimal Control Theory [pdf]
  Lawrence Evans

• Control in an Information Rich World
  Richard Murray et alia

• Control Theory: from Classical to Quantum [pdf]
  Matthew R. James

• Feedback Control Theory [pdf]
  John Doyle, Bruce Francis, Allen Tannenbaum

• Feedback Systems: An Introduction for Scientists and Engineers
  Karl Åström, Richard Murray

• Linear Controller Design: Limits of Performance
  Stephen Boyd, Craig Barratt

• Linear Matrix Inequalities in Systems and Control Theory
  Stephen Boyd, Laurent El Ghaoui, Eric Feron, Venkataramanan Balakrishnan

• Mathematical Control Theory
  Eduardo Sontag

• Stochastic Optimal Control: The Discrete-Time Case
  Dimitri Bertsekas, Steven Shreve

• The Analysis of Feedback Systems [pdf]
  Jan C. Willems

• Unsolved Problems in Mathematical Systems and Control Theory
  Vincent Blondel, Alex Megretsky

Cryptography:

• Handbook of Applied Cryptography
  Alfred Menezes, Paul van Oorschot, Scott Vanstone

• Introduction to Modern Cryptography [pdf]
  Mihir Bellare, Phillip Rogaway

Differential Geometry:

• A Course in Riemannian Geometry [pdf]
  David R. Wilkins

• A Geometric Approach to Differential Forms
  David Bachman

• A Modern Course on Curves and Surfaces [pdf]
  Richard S. Palais

• Comparison Geometry
  Karsten Grove, Peter Petersen (editors)

• Functional Differential Geometry [pdf]
  Gerald Jay Sussman, Jack Wisdom

• Lecture Notes on Bundles and Connections
  Chris Wendl

• Manifolds and Differential Forms [pdf]
  Reyer Sjamaar

• Natural operations in Differential Geometry
  Ivan Kolar, Jan Slovak and Peter W. Michor

• Notes on Differential Geometry
  Balázs Csikós

• Notes on Differential Geometry [pdf]
  Noel J. Hicks

Discrete Mathematics:

• Analytic Combinatorics
  Philippe Flajolet, Robert Sedgewick

• Discrete Mathematics
  Jean Gallier

• Discrete Mathematics [pdf]
  Lovász, Vesztergombi

• Foundations of Combinatorics with Applications
  Edward A. Bender, S. Gill Williamson

• generatingfunctionology
  Herbert Wilf

• New Perspectives in Algebraic Combinatorics
  Louis J. Billera, Anders Björner, Curtis Greene, Rodica Simion, Richard P. Stanley (editors)

Dynamical Systems and ODEs:

• Invitation to Dynamical Systems
  Edward R. Scheinerman

• Ordinary Differential Equations and Dynamical Systems
  Gerald Teschl

• Optimization and Dynamical Systems [pdf]
  Uwe Helmke, John B. Moore

• Perturbation Theory of Dynamical Systems
  Nils Berglund

• Teoria Qualitativa das Equações Diferenciais [pdf]
  José Basto Gonçalves, Isabel Labouriau

• Theory of Ordinary Differential Equations [pdf]
  Christopher P. Grant

Economics:

• Economics and Language
  Ariel Rubinstein

• Economics in One Lesson
  Henry Hazlitt

• Lecture Notes in Microeconomic Theory [pdf]
  Ariel Rubinstein

• Modeling Bounded Rationality
  Ariel Rubinstein

Electromagnetics:

• Electromagnetic Field Theory
  Bo Thidé

• Electromagnetic Waves and Antennas
  Sophocles J. Orfanidis

• Finite-element Methods for Electromagnetics
  Stanley Humphries

Fourier and Harmonic Analysis:

• Harmonic Function Theory
  Sheldon Axler, Paul Bourdon, Wade Ramey

• The Fourier Transform and its Applications [pdf]
  Brad Osgood

Functional Analysis:

• Functional Analysis
  Paul Garrett

• Functional Analysis
  Gerald Teschl

• Nonlinear Functional Analysis
  Gerald Teschl

Game Theory & Combinatorial Games:

• Algorithmic Game Theory [pdf]
  Noam Nisan, Tim Roughgarden, Éva Tardos, Vijay Vazirani (editors)

• Games of No Chance
  Richard Nowakowski (editor)

• Games of No Chance II
  Richard Nowakowski (editor)

• Games of No Chance III
  Michael H. Albert, Richard J. Nowakowski (editors)

• Political Game Theory [pdf]
  Nolan McCarty, Adam Meirowitz

Geometry:

• Combinatorial and Computational Geometry
  Jacob E. Goodman, János Pach, Emo Welzl (editors)

• Computational Geometry [pdf]
  David Mount

• Flavors of Geometry
  Silvio Levy (editor)

• Geometric Asymptotics
  Victor Guillemin, Shlomo Sternberg

• Lectures on Convex Sets [pdf]
  Niels Lauritzen

• Lectures on Discrete and Polyhedral Geometry [pdf]
  Igor Pak

• The Foundations of Geometry
  David Hilbert

Graph Theory:

• Fractional Graph Theory [pdf]
  Daniel Ullman, Edward Scheinerman

• Graph Theory [pdf]
  Reinhard Diestel

• Graph Theory with Applications [pdf]
  Bondy, Murty

• Spectra of graphs [pdf]
  Andries E. Brouwer, Willem H. Haemers

Imaging:

• Imaging the Earth’s Interior
  Jon Claerbout

• Principles of Computerized Tomographic Imaging
  Avinash C. Kak, Malcolm Slaney

Information Theory:

• Algorithmic Information Theory [pdf]
  Greg Chaitin

• Entropy and Information Theory
  Robert M. Gray

• Information-Theoretic Incompleteness [pdf]
  Greg Chaitin

• Information Theory, Inference, and Learning Algorithms
  David J.C. MacKay

Linear Algebra:

• An Introduction To Linear Algebra [pdf]
  Kenneth Kuttler

• Linear Algebra
  Jim Hefferon

• Linear Algebra done wrong [pdf]
  Sergei Treil

Machine Learning:

• Gaussian Processes for Machine Learning
  Carl Edward Rasmussen, Christopher K. I. Williams

• The Elements of Statistical Learning
  Trevor Hastie, Robert Tibshirani, Jerome Friedman

Markov Chains:

• Markov Chains and Mixing Times
  David A. Levin, Yuval Peres, Elizabeth L. Wilmer

• Markov Chains and Stochastic Stability
  Sean Meyn, Richard Tweedie

• Reversible Markov Chains and Random Walks on Graphs
  David Aldous, James Allen Fill

Mathematical Physics:

• Elementary Mechanics from a mathematician’s viewpoint [pdf]
  Michael Spivak

• Mathematical Methods in Quantum Mechanics
  Gerald Teschl

Miscellaneous:

• Book of Proof
  Richard Hammack

• Cinq siècles de mathématiques en France [pdf]
  Marcel Berger

• Computational Semantics with Functional Programming
  Jan van Eijck, Christina Unger

• Handbook of Mathematical Functions
  Milton Abramowitz, Irene A. Stegun

• Lie Algebras [pdf]
  Shlomo Sternberg

• Mathematics for the Physical Sciences
  Herbert Wilf

• Mathematics of the Rubik’s cube [pdf]
  David Joyner

• Music: a Mathematical Offering
  David Benson

• Networks, Crowds, and Markets
  David Easley, Jon Kleinberg

• Radon Transform [pdf]
  Sigurdur Helgason

• Récoltes et Semailles
  Alexandre Grothendieck

• Security Engineering
  Ross Anderson

• Sustainable Energy – without the hot air
  David J.C. MacKay

• The Mathematics of Gambling
  Edward Thorp

• The Science of Computing [pdf]
  Carl Burch

• The Scottish Book
  Stefan Banach, Stanisław Ulam, Hugo Steinhaus, et alia

• Traveling Wave Solutions of Parabolic Systems
  Aizik I. Volpert, Vitaly A. Volpert, Vladimir A. Volpert

Number Theory:

• A Computational Introduction to Number Theory and Algebra
  Victor Shoup

• Algorithmic Number Theory
  Joseph P. Buhler, Peter Stevenhagen (editors)

• An Introduction to the Theory of Numbers
  Leo Moser

• Elementary Number Theory [pdf]
  Edwin Clark, Jim Hefferon

• Elementary Number Theory
  William Stein

• Modular Forms: A Computational Approach
  William Stein

Optimization:

• Convex Optimization
  Stephen Boyd, Lieven Vandenberghe

• Convex Optimization & Euclidean Distance Geometry
  Jon Dattorro

• Lecture Notes on Optimization [pdf]
  Pravin Varaiya

• Linear Programming – A Concise Introduction [pdf]
  Thomas S. Ferguson

• Network Optimization: Continuous and Discrete Models
  Dimitri Bertsekas

• Optimization Algorithms on Matrix Manifolds
  Absil, Mahony, Sepulchre

• Semidefinite Programming
  Stephen Boyd, Lieven Vandenberghe

Partial Differential Equations:

• Hilbert Space Methods for Partial Differential Equations
  R. E. Showalter

• Partial Differential Equations of Applied Mathematics [pdf]
  D.H. Sattinger

• Partial Differential Equations of Mathematical Physics [pdf]
  William Symes

Photonics:

• Photonic Crystals: Molding the Flow of Light
  John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade

Probability Theory:

• Probability Theory: the Logic of Science
  E.T. Jaynes

• Probability: Theory and Examples
  Rick Durrett

Quantum Field Theory:

• Fields: Classical and Quantum Field Theory
  Warren Siegel

• Introduction to Algebraic and Constructive Quantum Field Theory
  John C. Baez, Irving E. Segal, Zhengfang Zhou

• Quantum Field Theory
  Mark Srednicki

Quantum Mechanics:

• Notes on Quantum Mechanics [pdf]
  Klaus Schulten

• Lecture Notes in Quantum Mechanics
  Doron Cohen

Real Analysis:

• Elements of Linear and Real Analysis
  Stephen Semmes

• Introduction to Real Analysis
  William F. Trench

• Theory of functions of a real variable [pdf]
  Shlomo Sternberg

Representation Theory:

• Introduction to Representation Theory [pdf]
  Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Elena Udovina, Dmitry Vaintrob

Set Theory:

• Descriptive Set Theory [pdf]
  Yiannis N. Moschovakis

• Undergraduate Set Theory [pdf]
  Ernest Schimmerling

Signal Processing:

• An Introduction to Frames [pdf]
  Jelena Kovačević, Amina Chebira

• An Introduction to Statistical Signal Processing
  Robert M. Gray, Lee D. Davisson

• Fundamentals of Geophysical Data Processing [pdf]
  Jon Claerbout

• Introduction to Digital Speech Processing [pdf]
  Lawrence R. Rabiner, Ronald W. Schafer

• Mixed-Signal and DSP Design Techniques
  Walt Kester

• Modern Signal Processing
  Daniel Rockmore, Dennis Healy (editors)

• Optimum Signal Processing
  Sophocles J. Orfanidis

• The Scientist and Engineer’s Guide to Digital Signal Processing
  Steven W. Smith

• The Theory of Linear Prediction
  P.P. Vaidyanathan

• Wavelets and Subband Coding
  Martin Vetterli, Jelena Kovačević

Statistics:

• Introduction to Statistical Thought
  Michael L. Lavine

• Tensor Methods in Statistics
  Peter McCullagh

Statistical Mechanics:

• Information, Physics and Computation
  Andrea Montanari, Marc Mézard

• Statistical Mechanics [pdf]
  Daniel Styer

• Statistical Mechanics: Entropy, Order Parameters, and Complexity
  James P. Sethna

Stochastic Processes:

• An Exploration of Random Processes for Engineers
  Bruce Hajek

• An Introduction to Stochastic Differential Equations [pdf]
  Lawrence C. Evans

• Probability, Random Processes, and Ergodic Properties
  Robert M. Gray

• Stochastic Calculus and Finance [pdf]
  Steven Shreve

Topology:

• Topology without tears
  Sidney A. Morris

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If you find any typos or broken links, please let me know. To the best of my knowledge, all the books / lecture notes above were willingly made available by their authors. If you find evidence of copyright infringement, please inform me immediately.