Book:Lecture Notes

Lecture Notes

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Abstract Algebra

 * R.B. Ash: Abstract Algebra
 * Paul Garrett: Abstract Algebra
 * Paul Garrett: Intro to Abstract Algebra (Solutions)
 * D. Surowski: A Workbook in Higher Algebra

Linear Algebra

 * H. Connell: Elements of Abstract and Linear Algebra
 * J. Hefferon: Linear Algebra
 * A. Baker: Basic Linear Algebra
 * W.W.L. Chen: Linear Algebra

Group Theory

 * J.S. Milne: Group Theory
 * P. Cvitanović: Group Theory: Birdtracks, Lie's and Exceptional Groups
 * Paul Garrett: Buildings, BN-Pairs, Hecke Algebras, Classical Groups
 * R.B. Howlett: Miscellaneous Facts About Coxeter Groups
 * Introduction to Group Theory
 * A. Baker: Groups and Symmetry

Representation Theory

 * A. Baker: Representations of Finite Groups
 * C. Teleman: Representation Theory
 * P. Etingof, O. Golberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, and E. Yudovina: Introduction to representation theory

Universal Algebra

 * G.M. Bergman: An Introduction to Universal Algebra
 * S. Burris and H.P. Sankappanavar: A Course in Universal Algebra
 * M. Valeritoe: Lectures on Universal Algebra

Lie Groups

 * B.C. Hall: An Elementary Introduction to Groups and Representations
 * Paul Garrett: Lie Algebras and Lie Groups
 * I. Avramidi: Notes on Lie Groups
 * R.L. Bryant: An Introduction to Lie Groups and Symplectic Geometry
 * A. Cap: Lie Groups

Galois Theory

 * J.S. Milne: Fields and Galois Theory
 * D. Wilkins: Galois Theory
 * A. Baker: An Introduction to Galois Theory
 * J.P. Serre: Topics in Galois Theory
 * M. Reid: Galois Theory
 * S.R. Ghorpade: Notes on Galois Theory

Lattice Theory

 * Stanford handout on Lattice theory

Commutative Algebra

 * R.B. Ash: Commutative Algebra
 * Paul Garrett: Homological and Commutative Algebra
 * D. Murfet: Matsumura: Commutative Algebra
 * S.R. Ghorpade: Lectures on Commutative Algebra

Category Theory

 * M. Fokkinga: A Gentle Introduction to Category Theory
 * M. Bar and C. Wells: Toposes, Triples and Theories
 * J. van Oosten: Basic Category Theory
 * D. Turi: Category Theory Lecture Notes
 * D.E. Rydeheard and R.M. Burstall: Computational Category Theory

Number Theory

 * W.W.L. Chen: Elementary Number Theory
 * W.W.L. Chen: Distribution of Prime Numbers
 * J.S. Milne: Algebraic Number Theory
 * R.B. Ash: Algebraic Number Theory
 * J.S. Milne: Modular Functions and Modular Forms
 * Paul Garrett: Modular Forms and L-Functions
 * I.V. Dolgachev: Modular Forms
 * J.S. Milne: Etale Cohomology
 * J.S. Milne: Class Field Theory
 * J.S. Milne: Complex Multiplication
 * J.S. Milne: Abelian Varieties
 * Paul Garrett: Number Theory
 * Paul Garrett: Cryptography and Number Theory
 * Paul Garrett: Coding Theory
 * A. Baker: An Introduction to $p$-adic Numbers and $p$-adic Analysis
 * A. Baker: Algebra and Number Theory
 * I. Connell: An Elliptic Curve Handbook

Algebraic Geometry

 * J.S. Milne: Algebraic Geometry
 * J.S. Milne: Algebraic Groups
 * I.V. Dolgachev: Introduction to Algebraic Geometry
 * I.V. Dolgachev: The McKay Correspondence
 * I.V. Dolgachev: Topics in Classical Algebraic Geometry
 * C. Weibel: An Introduction to Algebraic K-Theory

Differential Geometry

 * B. Csikós: Differential Geometry
 * G. Lugo: Differential Geometry
 * M. Kazarian: Differential Geometry
 * T. Shifrin: Differential Geometry: A First Course in Curves and Surfaces
 * D. Zaitsev: Differential Geometry: Lecture Notes
 * J.-P. Demailly: Complex Analytic and Diﬀerential Geometry

Complex Analysis

 * R.B. Ash: Complex Variables
 * Paul Garrett: Complex Analysis
 * G. Cain: Complex Analysis
 * H.V. McIntosh: Complex Analysis
 * W.W.L. Chen: Introduction to Complex Analysis

Real Analysis

 * R.B. Ash: Real Variables with Basic Metric Space Topology
 * S. Semmes: Elements of Linear and Real Analysis
 * J. Orr: Analysis WebNotes
 * I. Craw: Advanced Calculus and Analysis
 * W.W.L. Chen: Fundamentals of Analysis

Functional Analysis

 * W.W.L. Chen: Linear Functional Analysis
 * W.W.L. Chen: Introduction to Lebesgue Integration
 * T. Ward: Functional Analysis
 * Paul Garrett: Functional Analysis

Differential Equations

 * E.M. Harrell and J.V. Herod: Linear Methods of Applied Mathematics

Probability and Statistics

 * R.B. Ash: Lectures on Statistics
 * R.B. Ash: Basic Probability Theory
 * C. Grinstead and J. Snell: Introduction to Probability
 * N. Vaillant: Probability Tutorials

Complexity and Algorithms

 * C. Yap: Fundamental Problems in Algorithmic Algebra
 * C. Yap: Introduction to Complexity Classes
 * C. Yap: Robust Geometric Computation
 * C. Yap: Algorithmics
 * W.W.L. Chen: Discrete Mathematics

Combinatorics

 * M. Petkovsek, H. Wilf and D. Zeilberger: The Book A=B
 * H. Wilf: Generatingfunctionology
 * D. Feldman: Ramsey's Theorem and Ramsey Theory
 * Dynamic Surveys in Combinatorics

Basic Algebra

 * K. Kubota: College Algebra
 * D. Joyce: A Short Course in Trigonometry
 * T. Ward: Basic Mathematics
 * W.W.L. Chen: Miscellaneous Topics in First Year Mathematics
 * MathIsFun: College Algebra

Calculus

 * G. Cain and J. Herod: Multivariable Calculus
 * Harvey Mudd College Calculus Tutorials
 * D. Sloughter: Difference Equations to Differential Equations
 * P. Dawkins: Paul's Online Math Notes
 * W.W.L. Chen and X.T. Duong: Elementary Mathematics
 * W.W.L. Chen: First Year Calculus
 * W.W.L. Chen: Multivariable and Vector Analysis

Graph Theory

 * R. Diestel: Graph Theory

Dynamical Systems

 * G. Elert: The Chaos Hypertextbook
 * P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner, G. Vattay, N. Whelan and A. Wirzba: Chaos: Classical and Quantum
 * J. Milnor: Dynamics in One Complex Variable
 * P. Arnoux, V. Berthé, S. Ferenczi, S. Ito, C. Mauduit, M. Mori, J. Peyrière, A. Siegel, J.-I. Tamura and Z.-Y. Wen: Substitutions in Dynamics, Arithmetic and Combinatorics
 * T. Ward: Entropy of Compact Group Automorphisms
 * T. Ward: Valuations and Dynamics

Topology

 * C. Johnson and M. Burnett: Crystallographic Topology
 * S.A. Morris: Topology Without Tears

Algebraic Topology

 * A. Hatcher: Vector Bundles and K-Theory
 * T. Ward: Algebraic Topology

Logic

 * S. Bilaniuk: A Problem Course in Mathematical Logic

MIT Online Materials

 * http://ocw.mit.edu/courses/mathematics/