The theory of finite fields is a branch of algebra that has come to the fore becasue of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching ciruits. This book is devoted entirely to the theory of finite fields, and it provides comprehensive coverage of the literature. Bibliographical notes at the end of each chapter give an historical survey of the development of the subject. Workd out examples and lists of exercises found throughout the book make it useful as a text for advanced level courses.