See the last few pages of Baues: Homotopy types, for a brief intro and references, including def of Sullivan minimal models.
Hess: Rational HT, a brief introd
http://ncatlab.org/nlab/show/rational+homotopy+theory
For a physicist’s intro to rational homotopy theory, see Crane: Model categories and quantum gravity
Bousfield and Gugenheim: On PL de Rham theory and rational homotopy type. Memoirs of the AMS 8 (no el copy), 1976. “Bridges the gap between Quillen’s and Sullivan’s approaches to rational homotopy theory”.
arXiv:1211.1647 Dewformation theory and rational homotopy type fra arXiv Front: math.AT av Mike Schlessinger, Jim Stasheff We regard the classification of rational homotopy types as a problem in algebraic deformation theory: any space with given cohomology is a perturbation, or deformation, of the “formal” space with that cohomology. The classifying space is then a “moduli” space — a certain quotient of an algebraic variety of perturbations. The description we give of this moduli space links it with corresponding structures in homotopy theory, especially the classification of fibres spaces with fixed fibre F in terms of homotopy classes of maps of the base B into a classifying space constructed from the monoid of homotopy equivalences of F to itself. We adopt the philosophy, later promoted by Deligne in response to Goldman and Millson, that any problem in deformation theory is “controlled” by a differential graded Lie algebra, unique up to homology equivalence (quasi-isomorphism) of dg Lie algebras. Here we extend this philosophy further to control by sh-Lie-algebras.
Bousfield-Kan p 10 expresses the hope for an R-homotopy theory, for any subring R of the rationals, or for .
nLab page on Rational homotopy theory