Issues in topological gauge theory

We discuss topological theories, arising from the general N = 2 twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of sources and study the mixing between the various p-observables. We present the twisted superfield formalism which makes duality transformations transparent. We propose a scheme which uniquely fixes all the contact terms. We derive a formula for the correlation functions of p-observables on the manifolds of generalized simple type for 0 ≤ p ≤ 4 and on some manifolds with b⁺₂ = 1. We study the theories with matter and explore the properties of universal instantons. We also discuss the compactifications of higher dimensional theories. Some relations to sigma models of type A and B are pointed out and exploited.