First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation theory, including a masterly treatment of topics such as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations. These and many other subjects are treated extremely thoroughly, starting with basic definitions and results and proceeding to many important and crucial developments. Numerous examples and exercises help the reader of this unsurpassed book to master this important area of mathematics.