  We propose an explanation via string theory of the correspondence between the
Coulomb branch of certain three-dimensional supersymmetric gauge theories and
certain moduli spaces of magnetic monopoles. The same construction also gives
an explanation, via $SL(2,\Z)$ duality of Type IIB superstrings, of the
recently discovered ``mirror symmetry'' in three dimensions. New phase
transitions in three dimensions as well as new infrared fixed points and even
new coupling constants not present in the known Lagrangians are predicted from
the string theory construction. An important role in the construction is played
by a novel aspect of brane dynamics in which a third brane is created when two
branes cross.
