The theory of finite fields is a branch of algebra with diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching circuits. This updated second edition 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 a historical survey of the development of the subject. Worked examples and lists of exercises throughout the book make it useful as a text for advanced level courses for students of algebra.