  We present a first step towards generalizing the work of Seiberg and Witten
on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups.
Specifically, we propose a particular sequence of hyperelliptic genus $n-1$
Riemann surfaces to underly the quantum moduli space of $SU(n)$ N=2
supersymmetric gauge theory. These curves have an obvious generalization to
arbitrary simply laced gauge groups, which involves the A-D-E type simple
singularities. To support our proposal, we argue that the monodromy in the
semiclassical regime is correctly reproduced. We also give some remarks on a
possible relation to string theory.
