Our purpose in this book is to give a direct and readable account of the basic concepts and techniques of the theory of modular representations of finite groups and some significant applications. If we have succeeded in our aim, then the book will be useful both as a textbook for students and as an introductory guide to the rather extensive literature in the subject.
The theory of modular representations has a reputation of being much more difficult than the theory of ordinary representations, and to some extent this reputation is justified. At least at the beginning, the modular theory requires a more sophisticated background in algebra, and it takes a little longer to reach the stage where we can apply the theory. On the other hand, a knowledge of elementary properties of rings and modules up to, say, the Artin-Wedderburn structure theorem for Artinian rings together with a reasonable background in the theory of finite groups will be adequate prerequisite for almost all that we shall do in this book.
At the same time we shall see that there are serious applications of the theory at quite an early stage, and before the end of the book we shall be using the theory to prove some of the deep and important results on finite groups that have been obtained only in this way.
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