In mathematics, rational homotopy theory is the study of the rational homotopy type of a space, which means roughly that one ignores all torsion in the homotopy groups. It was started by Dennis Sullivan (1977) and Daniel Quillen (1969).
Rational homotopy types of simply connected spaces can be identified with (isomorphism classes of) certain algebraic objects called minimal Sullivan algebras, which are commutative differential graded algebras over the rational numbers satisfying certain conditions.
The standard textbook on rational homotopy theory is (Félix, Halperin & Thomas 2001).
Read more about Rational Homotopy Theory: Rational Spaces, Sullivan Algebras, The Sullivan Minimal Model of A Topological Space, Formal Spaces, Examples, External Links
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