Andr\'e-Quillen cohomology and rational homotopy of function spaces

We develop a simple theory of Andr\'e-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent $CW$-complexes. This puts certain results of Sullivan in a more conceptual framework.