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We propose a unified scheme for finding the hyperelliptic curve of $N=2$ SUSY
YM theory with any Lie gauge groups. Our general scheme gives the well-known
results for the classical gauge groups and the exceptional $G_2$ group. In
particular, we present the curve for the exceptional gauge groups $F_4,
E_{6,7,8}$ and check the consistency condition for them. The exact monodromies
and the dyon spectrum of these theories are determined. We note that for any
Lie gauge groups, the exact monodromies could be obtained only from the
Cartan matrix.
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