In this thesis we investigate the canonical structure of Topologically Massive Gravity (TMG) . T his theory is constructed by adding a Chern-Symons term to the ordinary Hilbert-Einstein action with cosmological constant . We use the formalism of noncoordinate basis in which the vierbein and spin connections are used instead of metric and Cristofel symbols .\\\\ We begin by studding in details the form structure of gravity and Chern-Symons term. We see that the underlying gauge group of the theory is SO(2,2), ISO(2,1) for $ \\Lambda 0 $ and $ \\Lambda =0$ respectively. Topological massive gravity possesses one degr of freedom at the linear level. This is in contrast with the pure gravity in three dimension which contains no dynamical degree's of freedom. \\\\ Our main interests in this thesis is counting the number of degrees of freedom . The best way for this goal is the Hamiltonian formalism. There is not a convergent set of result in the literature. We used the formalism of first order Lagrangian recognized as Fadeev-Jackiw approach or symplectic approach. The TMG theory begins with 27 variables where 9 of them can be considered as Lagrange multipliers. We find 9 primary constraints among the 18 remaining variables. After a lengthy calculation we find that only 3 of primary constraint are first ltr"
