  We classify all the solutions to the elliptic Toda system associated to a
general simple Lie algebra with singular sources at the origin and with finite
energy. The solution space is shown to be parametrized by a subgroup of the
corresponding complex Lie group. We also show the quantization result for the
finite integrals. This work generalizes the previous works in [Lin, Wei, Ye]
and [Nie] for Toda systems of types $A$ and $B, C$. However, a more
Lie-theoretic method is needed here for the general case, and the method relies
heavily on the structure theories of the local solutions and of the
$W$-invariants for the Toda system. This work will have applications to
nonabelian Chern-Simons-Higgs gauge theory and to the mean field equations of
Toda type.
