  In this paper we continue the programme of topologically twisting N=2
theories in D=4, focusing on the coupling of vector multiplets to N=2
supergravity. We show that in the minimal case, namely when the special
geometry prepotential F(X) is a quadratic polynomial, the theory has a so far
unknown on shell U(1) symmetry, that we name R-duality. R-duality is a
generalization of the chiral-dual on shell symmetry of N=2 pure supergravity
and of the R-symmetry of N=2 super Yang-Mills theory. Thanks to this, the
theory can be topologically twisted and topologically shifted, precisely as
pure N=2 supergravity, to yield a natural coupling of topological gravity to
topological Yang-Mills theory. The gauge-fixing condition that emerges from the
twisting is the self- duality condition on the gauge field-stength and on the
spin connection. Hence our theory reduces to intersection theory in the
moduli-space of gauge instantons living in gravitational instanton backgrounds.
We remark that the topological Yang-Mills theory we obtain by taking the flat
space limit of our gravity coupled Lagrangian is different from the Donaldson
theory constructed by Witten. Whether this difference is substantial and what
its geometrical implications may be is yet to be seen. We also discuss the
topological twist of the hypermultiplets leading to topological quaternionic
$\sigma$-models. The instantons of these models, named by us hyperinstantons,
correspond to a notion of triholomorphic mappings discussed in the paper.
