An introduction to abstract algebra : sets groups rings and fields This book is a textbook for a semester long or year long introductory course in abstract algebra at the upper undergraduate or beginning graduate level. It treats set theory group theory ring and ideal theory and field theory (including Galois theory) and culminates with a treatment of Dedekind rings including rings of algebraic integers. In addition to treating standard topics it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers with in particular distinctive treatments of factorization theory in integral domains and of Galois theory. As an introduction it presupposes no prior knowledge of abstract algebra but provides a well motivated clear and rigorous treatment of the subject illustrated by many examples. Written with an eye toward number theory it contains numerous applications to number theory (including proofs of Fermats theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular. Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further