The Hilbert- Ein stein action in 3 dimensions has no dynamical degree of freedom . In 1982 Deser , Jackiw and Templeton added the so called Chern-Simons term to Hilbert- Ein stein and showed that under linearization the corresponding model (recognized as topologocally massive gravity) possesses one massive degree of freedom . Appearing of dynamical degrees of freedom in a 3 - dimensional gravity theory bring attention to this model and to a set of models obtained by generalizing it . However , it is also possible to write 4-dimensional analog of TMG . In this thesis we have studied the dynamical behaviour of TMG in 3 dimensions and its 4-dimensional conterpart . In the framework of vierbeins variables , the action of TMG contains velocities just in the linear form . In other words , we have a first order lagrangian (FOL) . In order to investigate the canonical structure of a FOL one needs to make use of the " symplectic approach " of constrained systems , first proposed by Fadeev and Jackiw . Our next task in this thesis is to apply the symplectic approach in order to study the Hamiltonian structure of TMG . As our main result we found that the theory (in the original nonlinearized version) possesses 6 dynamical degrees of freedom in its phase space , which is equivalent to 3 degrees of freedom in the metrics formalism .