  An elementary theory is presented for solving the Sutherland model with
arbitrary internal symmetry such as SU($\nu$) or a supersymmetry SU($\nu,
\mu$). The ground state wave function and all the energy levels are derived.
One starts with solving a variant of the model with distinguishable particles,
and then (anti)symmetrizes the solution. The theory is also applied to various
lattice versions of the model. It is proved that the Gutzwiller-type wave
function is not only an eigenstate of the supersymmetric \it t-J \rm model, but
is indeed the ground state.
