Dummit D., Foote R. Abstract Algebra 3ed 2004

Textbook in PDF format

Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.* The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.
Preliminaries
Group Theory
Introduction to Groups
Subgroups
Quotient Groups and Homomorphisms
Group Actions
Direct and Semidirect Products and Abelian Groups Direct Products
Further Topics in Group Theory
Ring Theory
Introduction to Rings
Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
Polynomial Rings
Modules and Vector Spaces
Introduction to Module Theory
Vector Spaces
Modules over Principal Ideal Domains
Field Theory and Galois Theory
Field Theory
Galois Theory
An Introduction to Commutative Rings, Algebraic Geometry, and Homological Algebra
Commutative Rings and Algebraic Geometry
Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
Introduction to Homological Algebra and Group Cohomology
Introduction to the Representation Theory of Finite Groups
Representation Theory and Character Theory
Examples and Applications of Character Theory