of quasi-isomorphisms of dg-algebras.
In rational homotopy theory rational topological spaces are encoded in their dg-algebras of Sullivan forms. A simply connected topological space whose dg-algebra of Sullivan forms is formal is called a formal topological space. (One can also say a formal rational space, to distinguish from the unrelated formal spaces in formal topology.) Such a space represents a formal homotopy type.
compact Kähler manifolds (e.g. smooth projective varieties);
classifying spaces of Lie groups;
some homogeneous spaces
the unstable Thom spaces and
the space ,
whose Sullivan minimal model is the dg-algebra on a single degree-2 generator with trivial differential.
For an early discussion of formal dg-algebras in the context of rational homotopy theory see section 12 of
A survey is around definition 2.1 of