In this thesis we investigate the constraint analysis of the New Massive Gravity (NMG) by using Hamiltonian Method in Palatini approach, Topologically Massive Gravity (TMG) and Topologically Massive Spin 3 Theories by using Symplectic method. Constraint analysis of NMG is done here by using Hamiltonian Method in Palatini approach. It's shown that there is 2 degrees of freedom out of 6 components of metric tensor. This result is compatible with vector massive graviton which is due to linearization of this theory (Fierz-Pauli). To study constraint structure of TMG and it's spin 3 partner, we use Symplectic method. This method had never been used to analysis of these two theories. The equivalency of this method with commonly used method which is made by Dirac, is approved in some works. If we use Dreibeins and Spin connection formalism of TMG, we get 4 degrees of freedom. For spin 3 TMG we showed that by using Symplectic method we can simplify the algebras among basic variables. To achieve this simplification we introduce for first time, the new Darabaux coordinate basis. In this basis some of basic variables (without any requirement to momentum conjugate definition) play the role of momentum conjugate. This reduces dimension of phase space in contrast to the Hamiltonian method.