From reviews of the German Edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions. One who completes this text not only gains an appreciation of both the depth and the breadth of the theory of finite groups, but also witnesses the evolutionary development of concepts that form a basis for current investigations. This is accomplished by providing a thread that permits a natural flow from one concept to another rather than compartmentalizing. Operators on sets and groups are introduced early and used effectively throughout. The bibliography provides excellent supplemental support." H. Bechtell, Mathematical Reviews "Altogether, we have a well written book, which gives an introduction into the field and furthermore shows us one of the most active recent areas of research. This is the first book which shows us the amalgam method and moreover shows us how it works. Maybe it can get the same influence on group theory today as Gorenstein's famous book got in the late sixtees and seventees. This book should be in any library." G. Stroth, Zentralblatt