  This work explores the deformation theory of algebraic structures in a very
general setting. These structures include commutative, associative algebras,
Lie algebras, and the infinity versions of these structures, the strongly
homotopy associative and Lie algebras. In all these cases the algebra structure
is determined by an element of a certain graded Lie algebra which plays the
role of a differential on this algebra. We work out the deformation theory in
terms of the Lie algebra of coderivations of an appropriate coalgebra structure
and construct a universal infinitesimal deformation as well as a miniversal
formal deformation. By working at this level of generality, the main ideas
involved in deformation theory stand out more clearly.
