A very well known theorem by de Rham says that the real cohomology of a smooth manifold $X$ may be computed from the algebra $\Omega_{DR}(X)$ of differential forms on $X$. As an important corollary of his theory, Sullivan proves in fact that this algebra contains much more topological information about $X$. For instance, if $X$ is simply connected, the algebra gives the whole "real homotopy type" of $X$ (that is the groups $\Pi_{n}(X)\otimes \mathbb{R}$ and the real Postnikov invariants). This result may be generalized to the case of "nilpotent" spaces, that is to spaces whose fundamental group is nilpotent and acts nilpotently on higher homotopy groups.
The principal tool,making the theory very efficient and computable for the applications, is that of minimal algebra (which is, in some sense, the algebraic counterpart to the Postnikov decomposition of a space) : to any topological space $X$, Sullivan associates some commutative differential graded algebra $A_{\mathbb{Q}} (X)$ over ($\mathbb{Q}$ (improvment to ($\mathbb{Q}$ of a construction made over $\mathbb{R}$ by Thom and Whitney). Then to any commutative $DGA$, $A$, over a field $k$ with characteristic $0$, Sullivan associates its "minimal" model $\mathcal{M}_{A}$, and explains (at least if $X$ is nilpotent) how to read the rational homotopy type of $X$ on $\mathcal{M}_{{A}_{\mathbb{Q}}(X)}$. Furthermore, if $X$ is a smooth manifold, he proves $\mathcal{M}_{\Omega_{DR}(X)} = \mathcal{M}_{A_{\mathbb{Q}}(X)} \underset{\mathbb{Q}}{\otimes}{\mathbb{R}}$.