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"This book presents the solution of a long-standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on commutative algebra, cohomology of groups and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. "

"Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups, the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided."

"This is the proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 - 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations, theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups."

"This book acknowledges the varied incarnations of the fundemental group, pro-finite, L-adic, p-adic, pro-algebraic and motivic. It explores a weaelth of topics that range from anabelian geometry (in particular the section conjecture), the L-adic polylogarithm, gonality questions of mudular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's nonabelian Chaubauty method and p-adic integration after Coleman."