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 Second 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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Anyone who has studied abstract algebra and linear algebra as an
undergraduate can understand this book. The first six chapters provide
material for a first course, while the rest of the book covers more
advanced topics. This revised edition retains the clarity of
presentation that was the hallmark of the previous editions.
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 Second 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.
