  The goal of this paper is to set up an obstruction theory in the context of
algebras over an operad and in the framework of differential graded modules
over a field. Precisely, the problem we consider is the following: Suppose
given two algebras A and B over an operad P and an algebra morphism from the
homology of A to the homology of B. Can we realize this morphism as a morphism
of P-algebras from A to B in the homotopy category? Also, if the realization
exists, is it unique in the homotopy category? We identify obstruction cocycles
for this problem, and notice that they live in the first two groups of operadic
Gamma-cohomology.
