The algebraic foundation of cohomological eld theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. A s such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, di erent moduli spaces are obtained by i n troducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occurring di erential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum eld theory, and the discrete Regge calculus.