  In this paper we discuss the question of integrating differential graded Lie
algebras (DGLA) to differential graded Lie groups (DGLG).
  We first recall the classical problem of integration in the context, and
present the construction for (non-graded) differential Lie algebras. Then, we
define the category of differential graded Lie groups and study its properties.
We show how to associate a differential graded Lie algebra to every
differential graded Lie group and vice-versa. For the DGLA $\to$ DGLG
direction, the main ``tools'' are graded Hopf algebras and Harish-Chandra pairs
(HCP) -- we define the category of graded and differential graded HCPs and
explain how those are related to the desired construction. We describe some
near at hand examples and mention possible generalizations.
