Duality in supersymmetric gauge theories

In these lectures we discuss various aspects of gauge theories with extended $N=2$ and $N=4$ supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low energy effective action for the light degrees of freedom in the $N=2$ super Yang-Mills theory and the conjecture, supported by some checks, that the $N=4$ super Yang-Mills theory is dual in the sense of Montonen-Olive.