The CRC Handbook of Finite Fields is a comprehensive reference book that covers the theory and applications of finite fields. It is not intended as an introductory textbook but rather as a compilation of the latest research and developments in the field. The book is organized into three parts, with Part I focusing on the history of finite fields from the 18th to 19th centuries. Part II contains 12 chapters that explore the theoretical properties of finite fields, including topics such as irreducible polynomials, primitive polynomials, bases, and exponential and character sums. Part III covers various applications of finite fields, including combinatorial structures, algebraic coding theory, and cryptography. The book also includes extensive references to recent books, conference proceedings, and tables of polynomials that are useful in the study of finite fields. The Handbook aims to provide a comprehensive resource for researchers and practitioners in the field of finite fields, with easy access to up-to-date facts and results.The CRC Handbook of Finite Fields is a comprehensive reference book that covers the theory and applications of finite fields. It is not intended as an introductory textbook but rather as a compilation of the latest research and developments in the field. The book is organized into three parts, with Part I focusing on the history of finite fields from the 18th to 19th centuries. Part II contains 12 chapters that explore the theoretical properties of finite fields, including topics such as irreducible polynomials, primitive polynomials, bases, and exponential and character sums. Part III covers various applications of finite fields, including combinatorial structures, algebraic coding theory, and cryptography. The book also includes extensive references to recent books, conference proceedings, and tables of polynomials that are useful in the study of finite fields. The Handbook aims to provide a comprehensive resource for researchers and practitioners in the field of finite fields, with easy access to up-to-date facts and results.