Why Abstract Algebra --
Operations --
The Definition of Groups --
Elementary Properties of Groups --
Subgroups --
Functions --
Groups of Permutations --
Permutations of a Finite Set --
Isomorphism --
Order of Group Elements --
Cyclic Groups --
Partitions and Equivalence Relations --
Counting Cosets --
Homomorphism --
Quotient Groups --
The Fundamental Homomorphism Theorem --
Rings: Definitions and Elementary Properties --
Ideals and Homomorphism --
Quotient Rings --
Integral Domains --
The Integers --
Factoring into Primes --
Elements of Number Theory (Optional) --
Rings of Polynomials --
Factoring Polynomials --
Substitution in Polynomials --
Extensions of Fields --
Vector Spaces --
Degrees of Field Extensions --
Ruler and Compass --
Galois Theory: Preamble --
Galois Theory: The Heart of the Matter --
Solving Equations by Radicals --
Appendix A: Review of Set Theory --
Appendix B: Review of the Integers --
Appendix C: Review of Mathematical Induction ; Answers to Selected Exercises.

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability