This text is based on a one-semester graduate course taught by the author at The Fields Institute in fall 1995 as part of the homotopy theory program which constituted the Institute's major program that year. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program.

The notes are divided into two parts: prerequisites and the course proper. This book collects in one place the material that a researcher in algebraic topology must know. The author has attempted to make this text a self-contained exposition. Precise statements and proofs are given of "folk" theorems which are difficult to find or do not exist in the literature.