Duality in N=2 SUSY Gauge Theories: low-energy effective action and BPS spectra

Lectures given at the Institut Henri Poincar\'e program ``Strings, Supergravity and M-theory", Paris, January 2001, 47 pages, 6 eps figures, LatexAfter an introduction to N=2 susy Yang-Mills theories, I review in some detail, for the SU(2) gauge group, how the low-energy effective action is obtained using duality and the constraints arising from the supersymmetry. Then I discuss how knowledge of this action, duality and certain discrete symmetries allow us to determine the spectra of stable BPS states at any point in moduli space. This is done for gauge group SU(2), without and with fundamental matter hypermultiplets which may have non-vanishing bare masses. In the latter case non-trivial four-dimensional CFTs arise at Argyres-Douglas type points