The theory of fields has traditionally been considered a basic part of abstract algebra. In modern mathematics, however, the abundance of algebraic ideas which have been introduced has established the importance of the theory of fields not only in algebra but throughout all areas of mathematics as well. There are many topics that require discussion in the mathematics courses frequently offered in colleges and universities. Consequently, it is not unusual to have too few lecture hours devoted to the theory of fields.
In view of this, the author wished to publish a book on field theory, rich in topical variety, necessitating few prerequisites, and conveniently sized, that would allow any student to advance his study.
In this book, it is assumed that the reader is familiar with the basic definitions and results on set theory and determinants, and therefore these results are stated explicitly and without proof. In addition, some basic results on group theory and ring theory will
be needed; proofs foij these results are given. Thus the main text of this volume initially consists of preliminaries on groups and rings (Chapters 1 and 2) and in subsequent chapters (Chapters 3 to 7) focuses on several important topics on
fields, such as algebraic and transcendental extensions, valuations, ordered fields, and Galois theory of algebraic extensions.