First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a fourth edition. It reflects the exciting developments in number theory during the past decades that culminated in the proof of Fermat's Last Theorem. An historical introduction and new material on the Catalan conjecture will be included. Intended as an upper level textbook, it is also eminently suited as a text for self-study.