  We study SYM gauge theories living on ALE spaces.
  Using localization formulae we compute the prepotential (and its
gravitational corrections) for SU(N) supersymmetric ${\cal N}=2, 2^*$ gauge
theories on ALE spaces of the $A_n$ type. Furthermore we derive the
Poincar\'{e} polynomial describing the homologies of the corresponding moduli
spaces of self-dual gauge connections. From these results we extract the ${\cal
N}=4$ partition function which is a modular form in agreement with the
expectations of $SL(2,\Z)$ duality.
