General relativity in (2+1)-dimensions is important because its mathematical is more simple than four dimensional gravity, so we considered some aspect of (2+1)-dimensional gravity and its diffrence with four dimensional gravity. Hamiltonain formalism has a special role in modern physics, so we studied canonical gravity by means of spacetime decomposition in ADM approach and it able us to counting degree of freedom in phase space , also we attend to the boundary term in canonical gravity. We calculate BTZ black hole solu tion by constrained systems and we showed that BTZ solution can be determined by gauge fixing in phase space. For the pu rpose of constructing a hamiltonian formalism for gravitational field coupled to matter, we considered LTB model. In this model, dust is the source of matter and assume that be inhomogene o u s and irrotational. I t is showed that under wh ich circumstance dust collapses can shapes the BTZ black hole with zero angular momentu m and how is the behavior of sigularity , even horizon and apparent horizon. F or constructing LTB Hamiltonian, we using constrained systems to calculating first and second 0cm 0cm 0pt"
