I was pleased to accept the publisher's invitation to prepare an enlarged second edition of my book.

The theory of group representations is a large field, and it was difficult to decide what topics should fill the additional space that had become available.

Several colleagues were kind enough to give advice and also to draw my attention to errors in the first edition. I am particularly grateful to A. A. Bruen, R. W. Carter, W. L. Edge and G. D. James for their valuable comments.

However, it was impossible to incorporate all their suggestions. A selection had to be made: in accordance with the principal aim of this text, I have continued to place the emphasis on group characters rather than on the underlying representations.

The new material includes further work on tensor products, arithmetical properties of character values and the criterion for real representations due to Frobenius and Schur.

Once again, I should like to express my appreciation to the officers of Cambridge University Press for their help and understanding during the somewhat lengthy process of completing my task.