This is a collection of 25 research articles, assembled in 1998 and 1999 during a semester organised by Centre de Recerca Matemàtica, and especially during the 1998 Barcelona Conference on Algebraic Topology. The potential reader should note that these are research articles and not expository ones: nevertheless, we strongly encourage the reader to read them, as they give a very good picture of contemporary research in modern homotopy theory and are written by prominent specialists in the field. Each article contains a short introduction and enough references to provide orientation in the subject. They will be indispensable for researchers in homotopy theory and attractive for postgraduate students starting to work in this direction.

The main topics covered are: abstract stable homotopy, model categories, homotopical localisations and cellular approximations, p-compact groups, modules over the Steenrod algebra, classifying spaces for proper actions of discrete groups, K-theory and other generalised cohomology theories, cohomology of finite and profinite groups, Hochschild homology, configuration spaces, Lusternik-Schnirelmann category, stable and unstable splittings.

Reviewer:

jiva