Abstract Algebra

Preliminaries

Part I Group Theory
* Introduction to Groups
* Subgroups
* Quotient Groups and Homomorphisms
* Group Actions
* Direct and Semidirect Products and Abelian Groups
* Further Topics in Group Theory

Part II Ring Theory
* Introduction to Rings
* Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
* Polynomial Rings

Part III Modules and Vector Spaces
* Introduction to Module Theory
* Vector Spaces
* Modules over Principal Ideal Domains

Part IV Field Theory and Galois Theory
* Field Theory
* Galois Theory

Part V An Introduction To Commutative Rings, Algabraic Geometry, and Homological Algebra
* Commutative Rings and Algebraic Geometry
* Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
* Introduction to Homological Algebra and Group Cohomology

Part IV Introduction To The Representation Theory of Finite Groups
* Representation Theory and Character Theory
* Examples and Applications of Character Theory

Appendix I Cartesian Products and Zorn's Lemma
Appendix II Category Theory Index