  We show how enhanced gauge symmetry in type II string theory compactified on
a Calabi--Yau threefold arises from singularities in the geometry of the target
space. When the target space of the type IIA string acquires a genus $g$ curve
$C$ of $A_{N-1}$ singularities, we find that an $SU(N)$ gauge theory with $g$
adjoint hypermultiplets appears at the singularity. The new massless states
correspond to solitons wrapped about the collapsing cycles, and their dynamics
is described by a twisted supersymmetric gauge theory on $C\times \R^4$. We
reproduce this result from an analysis of the $S$-dual $D$-manifold. We check
that the predictions made by this model about the nature of the Higgs branch,
the monodromy of period integrals, and the asymptotics of the one-loop
topological amplitude are in agreement with geometrical computations. In one of
our examples we find that the singularity occurs at strong coupling in the
heterotic dual proposed by Kachru and Vafa.
