The dynamics of the metric tensor as the fundumental field describing gravity , is one of the most important problems of physics. This can be achieved in the Lagrangian as well as Hamiltonian formalism. In the Hamiltonian approach, however, one encounters some difficulties due to acceleration terms in the Lagrangian and boundry terms, as well. There are a few method to solve the problem of higher derivatives ( i.e grater than one ) in the Lagrangian of the general relativity, among which the Gamma-gamma formulation, the Palatini formulation and the vierbine formulation are studied in this thesis. Since some velocities are absent in the Lagrangian, the theory is a constrained theory. The constraint structure of a model can be studied in the framework of Dirac approach or Symplectic approach (Faddeev-Jackiw approach). In this thesis we study the Hamiltonian dynamics of the General relativity in both approaches. One of the most useful formulations of General relativity is the ADM approach. We review this approach in full details and construct the constraint structure of the theory in this framework. Some authors claim that the ADM formulation is not acceptable, since the ADM variables are not canonical. We have criticiz ed this claim and show that the ADM formulation is self-consistent.
