In the first part of this thesis we give an introduction to electric-magnetic duality and N=2 supersymmetry. After that we describe type II string theory instantons in the supergravity approximation. These instantons correspond to D-branes and NS-fivebranes wrapping non-vanishing cycles in the internal Calabi-Yau manifold. In the last chapter, we construct N=2 supersymmetric gauge theories involving both electric and magnetic (dyonic) charges. In these systems the electric-magnetic duality structure of the ungauged theories is preserved
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