Strom (mathematics, U. of Western Michigan) develops classical homotopy theory and some important developments that flow from it using the modern techniques of homotopy limits and co-limits. Students in their first or second year of graduate school are the intended readers, and they are assumed to be familiar with basic algebraic concepts such as groups and rings, and to have completed an introductory course in topology. There is ample material in the book for a typical two-semester sequence in homotopy theory or algebraic topology, with some left over at the end. It covers the language of categories; semi-formal homotopy theory; four topological inputs; targets as domains and domains as targets; cohomology and homology; cohomology, homology and fibrations; and vistas. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)