Free textbooks in Algebra
Abstract Algebra
- Lectures on Matrices by J. H. M. Wedderburn
- Abstract Algebra Theory and Applications by Thomas W. Judson. (LaTex source)
- Elementary Abstract Algebra by Edwin Clark
- Intro to Abstract Algebra by Paul Garrett
- Abstract Algebra done Concretely by Donu Arapura
- Elements of Abstract and Linear Algebra by Edwin H. Connell
- Abstract Algebra:The Basic Graduate Year by Robert Ash
- Geometric Group Theory by Cornelia Druţu and Michael Kapovich.
- Advanced Linear Algebra lecture notes by Keith Matthews (with real algorithm for the real Jordan form)
- Problems and Solutions in Commutative Algebra by Prof. Mahir Bilen Can
- A Primer of Commutative AlgebraJames by James S. Milne
- Expository Articles by James S. Milne.
- Basic Commutative Algebra by The Stacks Project
- Abstract Algebra - Number Theory, Group Theory, Galois Theory by Daviiid Wilkins
- 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
- Varieties of Lattices by Peter Jipsen and Henry Rose
- Commutator Theory for Congruence Modular Varieties by Ralph Freese and Ralph McKenzie
Algebraic Geometry
- Stacks project (the book) (Comprehensive graduate level introductory book on Algebraic Geometry from Stacks project
- Algebraic Geometry by Andreas Gathmann, Class Notes TU Kaiserslautern 2014
- Algebraic Geometry by J.S. Milne
- FOUNDATIONS OF ALGEBRAIC GEOMETRY by Ravi Vakil
- Algebraic geometry and projective differential geometry by Joseph M. Landsberg
- Introduction to Algebraic Geometry, Igor V. Dolgachev
- Metric Geometry and Geometric Group Theory by Lior Silberman
- REPRESENTATIONS OF REDUCTIVE GROUPS, by David Kazhdan
- Representations of finite groups, by David Kazhdan
- Lecture notes in Lie Algebras, by David Kazhdan
- Lecture notes in Representations of p-adic groups, by David Kazhdan
- Lecture notes in Category, by David Kazhdan
- Notes on Algebraic Geometry, J.S. Milne.
- Modular forms (Igor Dolgachev)
- Complex analytic and algebraic geometry - Jean-Pierre Demailly
- Moduli Spaces in Algebraic Geometry edited by L. Goettsche
- 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
- Determinantal rings by Winfried Bruns and Udo Vetter
Elliptic Curves
- An Introduction to theTheory of Elliptic Curves by Prof Joseph H. Silverman
- Elliptic curves by Miles Reid
- Elliptic curves, student project, Annegret Weng (ps 726K)
- Course Notes by Jim Milne: Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology
- The Modular curves X_{0}(N), Lecture notes by Bas Edixhoven
- Expository articles - Computing rational points on curves, Elliptic curves by Bjorn Poonen
Category Theory
- A Gentle Introduction to Category Theory, by Maarten M.Fokkinga
- Mixed Motives by Marc Levine
- David Madore's Math Page has a 50 page treatise on categories, in DVI and PS.
- 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
Lie Algebras
- Algebraic Groups and Discontinuous Subgroups by Armand Borel and George D. Mostow
- Linear Algebraic Groups - minor thesis by David Dumas
- Lie Algebras by Shlomo Sternberg