Résumé
The hypermultiplet moduli space of type IIB string theory compactified on a Calabi-Yau threefold is known to receive various instanton corrections and to carry an isometric action of SL(2,Z) duality group. The instanton corrections are most easily incorporated in the mirror type IIA formulation using the twistor space construction of quaternion-Kahler manifolds. In this talk I'll show how this construction can be turned into an explicitly S-duality invariant form thereby recovering the instanton corrections in type IIB and the quantum corrected mirror map between the physical fields of the two formulations. In particular, the case of D3-instantons reveals the importance of Mock theta series and period integrals which provide a holomorphic realization of S-duality in the twistor space.