  A quantization of classical deformation theory, based on the Maurer-Cartan
Equation $dS + \frac{1}{2}[S,S] = 0$ in dg-Lie algebras, a theory based on the
Quantum Master Equation $dS + \hbar \Delta S + \frac{1}{2} \{S,S\} = 0$ in
dg-BV-algebras, is proposed. Representability theorems for solutions of the
Quantum Master Equation are proven. Examples of "quantum" deformations are
presented.
