This monograph originated as a set of informal notes from a summer course taught by the present authors, together with Eric Friedlander, at the Istituto Matematico "Ulisse Dini" in Florence during the summer of 1972. Even though more formal expositions of Sullivan's theory have since
appeared, including the major original source, there has been a steady continuing demand for the old Florence notes. Moreover, one of us (J.M.) has become involved in the subject again through a series of lectures given at the University of Utah in January, 1980, together with joint work in
progress with James Carlson and Herb Clemens on a new type of application of the theory to algebraic geometry. Since the Florence notes represented an approach and point of view that does not appear in the literature, we decided to publish the present revised and corrected version.
The material in this monograph is outlined in the table of contents and is informally discussed in the introduction below. Here we should like to observe that the text roughly divides into two parts. The first seven chapters essentially constitute an introductory cause in algebraic topology with emphasis on homotopy theory. The main prerequisite is some familiarity with simplicial homology, covering spaces, and CW complexes.