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Advanced Abstract Algebra by Manonmaniam Sundaranar University
This book covers the following topics: Group, Normal subgroups and Quotient groups, homomorphism, isomorphism, Cayleys theorem, permutation groups, Sylow’s Theorems, Rings,Polynomial rings, Vector spaces, Extension field.
Author(s): Manonmaniam Sundaranar University
109 Pages 
These notes are a selfcontained introduction to Galois theory, for a student who has done a first course in abstract algebra. This note contains below topics, What is Galois Theory, Rings Polynomials, Roots and Irreducibility, Fields Basics Extensions and Concrete Examples, Rings Quotients, Fields Constructions and More Examples, Ruler and Compass Constructions, Vector Spaces Dimensions, Fields III Splitting Fields and Finite Fields, Ruler and Compass Constructions, Groups Soluble Groups and Simple Groups, Groups Symmetries of Fields, Vector Spaces Solving Equations, The Fundamental Theorem of Galois Theory, Applications of the Galois Correspondence, Not Solving Equations.
Author(s): Brent Everitt
94 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
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, Lagranges 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, Nonrigorous 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
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
Abstract Algebra Lecture Notes
This book explains the following topics, Group Theory, Subgroups, Cyclic Groups, Cosets and Lagranges Theorem, Simple Groups, Solvable Groups, Rings and Polynomials, Galois Theory, The Galois Group of a Field Extension, Quartic Polynomials.
Author(s): Dr. David R. Wilkins
NA Pages
These notes give a concise exposition of the theory of fields, including the Galois theory of finite and infinite extensions and the theory of transcendental extensions.
Author(s): J.S. Milne
130 Pages
Elements of Abstract and Linear Algebra
This is a foundational textbook on abstract algebra with emphasis on linear algebra. Covered topics are, Background and Fundamentals of Mathematics, Groups, Rings, Matrices and Matrix Rings and Linear Algebra.
Author(s): Edwin H. Connell
NA Pages