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It presents several themes of contemporary representation theory together with some new tools, such as stable ?-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary...

This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2).

It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite...

This monograph provides a thorough treatment of module theory, a subfield of algebra.

The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatorics and model theory.

The book is devoted to graduate students interested in algebra as well as to experts in module theory.