We study four dimensional N = 2 supersymmetric gauge theories with mat
ter multiplets. For all such models for which the gauge group is SU(2)
, we derive the exact metric on the moduli space of quantum vacua and
the exact spectrum of the stable massive states. A number of new physi
cal phenomena occur, such as chiral symmetry breaking that is driven b
y the condensation of magnetic monopoles that carry global quantum num
bers. For those cases in which conformal invariance is broken only by
mass terms, the formalism automatically gives results that are invaria
nt under electric-magnetic duality. In one instance, this duality is m
ixed in an interesting way with SO(8) triality.