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The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers.

Nilpotent groups. --- p-adic groups.

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Nilpotent groups. --- Representations of groups.

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Finite groups --- Nilpotent groups --- Solvable groups

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Group theory --- Nilpotent groups. --- Théorie des groupes

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The volume contains a collection of research articles by leading experts in group theory, and reports of several accessible surveys of recent research in the area. The compilation provide an overview of the diversity of themes and applications that interest today's group theorists. The topics covered in this volume include : character theory, combinatorial group theory, varieties of groups, conjugacy classes, profinite groups, graphs connected with groups, subgroup structure, representation theory.

Representations of groups --- Nilpotent groups --- Sylow subgroups --- Group theory