Introduction Table of Examples �� Homotopy Theory, Resolutions for Fibrations, and Plocal Spaces 0 Topological spaces 1 CW complexes, homotopy groups and coflbrations (a) CW complexes (b) Homotopy groups (c) Weak homotopy type (d) Cofibrations and NDR pairs (e) Adjunction spaces (f) Cones, suspensions, joins and smashes 2 Fibrations and topological monoids (a) Fibrations (b) Topological monoids and G-fibrations (c) The homotopy fibre and the holonomy action (d) Fibre bundles and principal bundles (e) Associated bundles, classifying spaces, the Borel construction and the holonomy fibration 3 Graded (differential) algebra (a) Graded modules and complexes (b) Graded algebras (c) Differential graded algebras (d) Graded coalgebras (e) When k is a field 4 Singular chains, homology and Eilenberg-MacLane spaces (a) Basic definitions, (normalized) singular chains (b) Topological products, tensor products and the dgc, C*(X;k) (c) Pairs, excision, homotopy and the Hurewicz homomorphism (d) Weak homotopy equivalences (e) Cellular homology and the Hurewicz theorem (f) Eilenberg-MacLane spaces 5 The cochain algebra C*(X;k) 6 (R,d)-modules and semifree resolutions (a) Semifree models (b) Quasi-isomorphism theorems 7 Semifree cochain models of a flbration 8 Semifree chain models of a G-flbration (a) The chain algebra of a topological monoid (b) Semifree chain models (c) The quasi-isomorphism theorem (d) The Whitehead-Serre theorem 9 p-local and rational spaces (a) p-local spaces (b) Localization (e) Rational homotopy type �� Sullivan Models �� Graded Differential Algebra (continued) �� Lie Models �� Rational Lusternik Schnirelmann Category �� The Rational Dichotomy References Index