LECTURES ON SPECIAL KAHLER GEOMETRY AND ELECTRIC-MAGNETIC DUALITY ROTATIONS

In these lecture I review the general structure of electric-magnetic d uality rotations in every even space-time dimension. In four dimension s, which is my main concern, I discuss the general issue of symplectic covariance and how it relates to the typical geometric structures inv olved by N=2 supersymmetry, namely Special Kahler geometry for the vec tor multiplets and either HyperKahler or Quaternionic geometry for the hypermultiplets. I discuss classical continuous dualities versus non- perturbative discrete dualities. How the moduli space geometry of an a uxiliary dynamical Riemann surface, (or Calabi-Yau threefold) relates to exact space-time dualities is exemplified in detail for the Seiberg Witten model of an SU(2) gauge theory.