  Chern-Simons formulation of the 2+1 dimensional Einstein gravity with
negative cosmological constant is investigated when the spacetime has the
topology ${\bf R}\times T^{2}$. The physical phase space is shown to be a
direct product of two sub-phase spaces having symplectic structures with
opposite signs. Each sub-phase space is found to be a non-Hausdorff manifold
plus a set of measure zero. Geometrical interpretation of each point in the
phase space is also given. A prescription to quantize this phase space is
proposed.
