Classical Galois theory : with examples

Galois theory is considered one of the most beautiful subjects in mathematics, but it is hard to appreciate this fact fully without seeing specific examples. Numerous examples are therefore included throughout this text, in the hope that they will lead to a deeper understanding and genuine appreciation of the more abstract and advanced literature on Galois theory. This book is strongly recommended to beginning graduate students who already have some background in abstract algebra, including elementary properties of groups, rings, and fields. The exposition and proofs are intended to present Galois theory as simply as possible. The large number of partially or fully solved examples is a special feature of the book. This chapter is intended to be a summary of some of the algebraic background we shall need later.