Abstract: I will present a generalization of the Lie group associated to Lie algebras, in the context of (nilpotent) differential graded Lie algebras. My construction generalizes a number of other known functors: the Deligne groupoid, the Dold-Kan functor, ... In this way, I obtain the first clear picture of how Quillen's theory of nilpotent rational homotopy types is a generalization of Lie's correspondence for nilpotent Lie algebras.