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Lecture Notes for Abstract Algebra I
This note covers the following topics: Group Theory, classification of cyclic subgroups, cyclic groups, Structure of Groups, orbit stabilizer theorem and conjugacy, Rings and Fields, homomorphism and isomorphism, ring homomorphism, polynomials in an indeterminant.
Author(s): James S. Cook
177 Pages 
Lecture Notes on Abstract Algebra by Aditya Sengupta
This note explains basic concepts like sets and relations and progressing to advanced topics such as group theory, rings, and fields also it covers fundamental theorems like Lagranges theorem and explores key concepts like permutations and quotient groups.
Author(s): Aditya Sengupta
86 Pages
Abstract Algebra Theory and Applications
This PDF covers the following topics related to Abstract Algebra : The Integers, Groups, Cyclic Groups, Permutation Groups, Cosets and Lagrange’s Theorem, Matrix Groups and Symmetry, Isomorphisms, Homomorphisms, The Structure of Groups, Group Actions, Vector Spaces.
Author(s): Thomas W. Judson
442 Pages
Abstract Algebra by Santiago Canez
This PDF covers the following topics related to Abstract Algebra : Introduction to Groups, Integers mod n , Dihedral Groups, Symmetric Groups, Homomorphisms, Group Actions, Some Subgroups, Cyclic Groups, Generating Sets, Zorn’s Lemma, Normal Subgroups, Cosets and Quotients, Lagrange’s Theorem, First Isomorphism Theorem, More Isomorphism Theorems, Simple and Solvable Groups, Alternating Groups, Orbit-Stabilizer Theorem, More on Permutations, Class Equation, Conjugacy in Sn, Simplicity of An, Sylow Theorems, More on Sylow, Applications of Sylow, Semidirect Products, Classifying Groups, More Classifications, Finitely Generated Abelian, Back to Free Groups.
Author(s): Santiago Canez, Northwestern University
103 Pages
Notes on Abstract Algebra by Scott M. LaLonde
This note explains the following topics: What is Abstract Algebra, The integers mod n, Group Theory, Subgroups, The Symmetric and Dihedral Groups, Lagrange’s Theorem, Homomorphisms, Ring Theory, Set Theory, Techniques for Proof Writing.
Author(s): Scott M. LaLonde
151 Pages
This note describes the following topics: Peanos axioms, Rational numbers, Non-rigorous proof of the fundamental theorem of algebra, polynomial equations, matrix theory, Groups, rings, and fields, Vector spaces, Linear maps and the dual space, Wedge products and some differential geometry, Polarization of a polynomial, Philosophy of the Lefschetz theorem, Hodge star operator, Chinese remainder theorem, Jordan normal form,Galois theory.
Author(s): Yum-Tong Siu
102 Pages
Introduction to Abstract Algebra by Alexander Paulin
This note explains the following topics: Sets and Functions, Factorization and the Fundamental Theorem of Arithmetic, Groups, Permutation Groups and Group Actions, Rings and Fields, Field Extensions and Galois Theory, Galois Theory.
Author(s): Alexander Paulin
83 Pages