Perhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's book is still considered to be a classic source for fundamental results on the representation theory for finite groups, the Burnside problem, extensions and cohomology of groups, $p$-groups and much more. For the student who has already had an introduction to group theory, there is much treasure to be found in Hall's Theory of Groups.
From the Preface to the First Edition (1976): "The present volume is intended to serve a dual purpose. The first ten chapters are meant to be the basis for a course in group theory, and exercises have been included at the end of each of these chapters. The last ten chapters are meant to be useful as optional material in a course or as reference material. When used as a text, the book is intended for students who have had an introductory course in modern algebra comparable to a course taught from Birkhoff and Mac Lane's A Survey of Modern Algebra. I have tried to make this book as self-contained as possible, but where background material is needed references have been given, chiefly to Birkhoff and Mac Lane."
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