I Homotopy Theory Resolutions for Fibrations and P- local Spaces. - 0 Topological spaces. - 1 CW complexes homotopy groups and cofibrations. - 2 Fibrations and topological monoids. - 3 Graded (differential) algebra. - 4 Singular chains homology and Eilenberg-MacLane spaces. - 5 The cochain algebra C*(X;$$\Bbbk $$. - 6 (R d) modules and semifree resolutions. - 7 Semifree cochain models of a fibration. - 8 Semifree chain models of a Gfibration. - 9 P local and rational spaces. - II Sullivan Models. - 10 Commutative cochain algebras for spaces and simplicial sets. - 11 Smooth Differential Forms. - 12 Sullivan models. - 13 Adjunction spaces homotopy groups and Whitehead products. - 14 Relative Sullivan algebras. - 15 Fibrations homotopy groups and Lie group actions. - 16 The loop space homology algebra. - 17 Spatial realization. - III Graded Differential Algebra (continued). - 18 Spectral sequences. - 19 The bar and cobar constructions. - 20 Projective resolutions of graded modules. - IV Lie Models. - 21 Graded (differential) Lie algebras and Hopf algebras. - 22 The Quillen functors C* and C. - 23 The commutative cochain algebra C*(LdL). - 24 Lie models for topological spaces and CW complexes. - 25 Chain Lie algebras and topological groups. - 26 The dg Hopf algebra C*(?X. - V Rational Lusternik Schnirelmann Category. - 27 Lusternik-Schnirelmann category. - 28 Rational LS category and rational cone-length. - 29 LS category of Sullivan algebras. - 30 Rational LS category of products and flbrations. - 31 The homotopy Lie algebra and the holonomy representation. - VI The Rational Dichotomy: Elliptic and Hyperbolic Spaces and Other Applications. - 32 Elliptic spaces. - 33 Growth of Rational Homotopy Groups. - 34 The Hochschild-Serre spectral sequence. - 35 Grade and depth for fibres and loop spaces. - 36Lie algebras of finite depth. - 37 Cell Attachments. - 38 Poincaré Duality. - 39 Seventeen Open Problems. - References. Language: English