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Chern-Simons formulation of 2+1 dimensional Einstein gravity with a negativecosmological constant is investigated when the spacetime has the topology $R\times T^{2}$. The physical phase space is shown to be a direct product of twosub-phase spaces each of which is a non-Hausdorff manifold plus a set withnonzero codimensions. Spacetime geometrical interpretation of each point in thephase space is also given and we explain the 1 to 2 correspondence with the ADMformalism from the geometrical viewpoint. In quantizing this theory, weconstruct a "modified phase space" which is a cotangnt bundle on a torus. Wealso provide a modular invariant inner product and investigate the relation tothe quantum theory which is directly related to the spinor representation ofthe ADM formalism. (This paper is the revised version of a previouspaper(hep-th/9312151). The wrong discussion on the topology of the phase spaceis corrected.)Comment: latex 28 page

Chern-Simons quantization of (2+1)-anti-de Sitter gravity on a torus