This is the second edition of the popular textbook on representation theory of finite groups. The authors have revised the text greatly and included new chapters on Characters of GL(2,q) and Permutations and Characters. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book.