Deformation theory via differential graded Lie algebras

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It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.

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Lie description of higher obstructions to deforming submanifolds (2005, background): “More precisely, to every differential graded Lie algebra L it is associated the functor [13,14,24,25] Def L : { local Artinian rings } → { Sets } gauge equivalence where m A is the maximal ideal of A .”
Lectures on deformations of complex manifolds (Deformations from differential graded viewpoint) (2005, background): “If we consider the above definition for a functor defined only for algebras concentrated in degree 0, then condition 3 is empty, while conditions 1 and 2 are essentially the classical Schlessinger’s conditions [67], [13], [52].”
Lectures on deformations of complex manifolds (2005, background): “9 – Historical survey The material Subsections 1, 2 and 3 is standard and well exposed in the literature about Lie algebras; in Subsections 4, 5 and 6 we follows the approach of [52], while the material of Subsections 7 and 8 comes from [53].”