This book is an outgrowth of an extensive paper “Torus actions, Combinatorial topology and homological algebra”, written by the authors and published in Uspekhi Mat. Nauk (Russian Math. Surveys) in 2000. It is yet another contribution to the recent rich interplay of combinatorics and convex geometry with algebraic geometry and topology. In Chapters 1-5, the authors review basic notions of both the combinatorial and topological side with a slight preference for combinatorial notions (which they consider less familiar to a prospective reader). The last three chapters are devoted to their own contribution, which is centred around moment angle complexes, their cohomology and to subspace arrangements. This is a useful book that will be of interest to the (algebraic) combinatorics community as well as to researchers in algebraic geometry and topology. It is a carefully written state of the art book.

Reviewer:

jneš