This book presents a new approach to the modular representation theory of a finite group G. Its aim is to provide a comprehensive treatment of the theory of G-algebras and to show how this theory is used to solve various problems in representation theory. Significant results have been obtained by means of this approach, which also sheds new light on modular representation theory. So it appears that a need has arisen for an expository book on the subject. I hope to meet this need and to introduce a wider audience to these new ideas.