  We show how BPS states of supersymmetric SU(2) Yang-Mills with matter -both
massless and massive- are described as self-dual strings on a Riemann surface.
This connection enables us to prove the stability and the strong coupling
behaviour of these states. The Riemann surface naturally arises from type-IIB
Calabi-Yau compactifications whose three-branes wrapped around vanishing
two-cycles correspond to one-cycles on this surface.
