Deformation theory via differential graded Lie algebras

This is an expository paper written in 1999 and published in Seminari di Geometria Algebrica 1998-1999, Scuola Normale Superiore (1999). Six years later some arguments used here appear quite naive and obsolete but, in view of the several citations that this paper has obtained in the meantime, I preferred don’t change the mathematical contents and to fix only some typos and minor mistakes. For a better and more recent treatment of these topics we refer to: M. Manetti, Lectures on deformations on complex manifolds, Rendiconti di Matematica 24 (2004) 1-183.