George W. Whitehead

This book consists of notes for a second-year graduate course in advanced topology given by Professor Whitehead at M.I.T. Presupposing a knowledge of the fundamental group and of algebraic topology as far as singular theory, it is designed to introduce the student to some of the more important concepts of homotopy theory. The book emphasizes (relative) CW-complexes, which the author believes to be the natural setting for obstruction theory, and follows the spirit of J.H.C. Whitehead's "combinatorial homotopy."

The writing bears the marks of authority of a mathematician who was actively involved in setting up the subject. Most of the papers referred to are at least twenty years old but this reflects the time when the ideas were established and one imagines that the situation will be different in the second volume. Because of the length, it is unlikely that many people will read this book from cover to cover, but it will be used for reading up on a particular topic or dipping into for sheer pleasure - and the fact that the details may not be quite as expected should add to the enjoyment.