Gary L. Mullen is a professor of mathematics at The Pennsylvania State University.Daniel Panario is a professor of mathematics at Carleton University.

"... a brilliant, monumental work on the state of the art in theory and applications of finite fields. It's a must for everyone doing research in finite fields and their related areas. ... It presents such a huge amount of information readily available and masterly presented. Editors, contributors, and the publisher are equally congratulated for providing such a beautiful result not only for the finite field community, but also for those from the applied areas, especially cryptographers and coding theorists."—Olaf Ninnemann, Berlin, in Zentralblatt MATH 1319"The handbook will be very useful for senior-level students, teachers, and researchers in mathematics and computer science. It will also be useful for scientists, engineers, and practitioners. The handbook is well organized. ... It is likely to become a standard reference book for the theory and applications of finite fields. ... It will be a very useful addition to the libraries of academic and research institutions."—S.V.Nagaraj, Chennai, India, in SIGACT News

• INTRODUCTION: History of Finite Fields. Introduction to Finite Fields. THEORETICAL PROPERTIES: Irreducible Polynomials. Primitive Polynomials. Bases. Exponential and Character Sums. Equations over Finite Fields. Permutation Polynomials. Special Functions over Finite Fields. Sequences over Finite Fields. Algorithms. Curves over Finite Fields. Miscellaneous Theoretical Topics. APPLICATIONS: Combinatorial. Algebraic Coding Theory. Cryptography. Miscellaneous Applications. Bibliography. Index.