  We show how to obtain the explicite form of the low energy quantum effective
action for $N=2$ supersymmetric Yang-Mills theory in the weak coupling region
from the underlying hyperelliptic Riemann surface. This is achieved by
evaluating the integral representation of the fields explicitly. We calculate
the leading instanton corrections for the group $SU(\nc), SO(N)$ and $SP(2N)$
and find that the one-instanton contribution of the prepotentials for the these
group coincide with the one obtained recently by using the direct instanton
caluculation.
