This thesis investigates geometric thermodynamics for black holes. First, one has introduced four different geometric thermodynamics models included in Weinhold and Ruppeiner models, Geometrothermodynamics and Q-metric. Then Poisson and Numbo bracket method has introduced in order to fluency in writing thermodynamics relations. It has been applied the concept of extrinsic curvature for hyper surfaces in geometric thermodynamic. The role of this quantity has been investigated in prediction of phase transition points and stable/unstable areas. The extrinsic curvature has been calculated for Pauli gas and some black holes, then has been showed correspondence of phase transition points and singularities of scalar curvature. This study investigates a new solution of Einstein gravity equations in (d+1) dimensional that is in based on generalization BTZ space-time to higher dimensions with toroidal horizons. This metric has considered for horizon topology, asymptotic and closed time like curves. Thermodynamic aspects of these solutions have been studied and some quantities such as entropy have been found in common approach and Solution Phase Space Method (M). Also, in the present study, we found interior solution for charged and uncharged cases and investigated completely their physical aspects. Studding of Newman-Janis algorithm in generalization of non rotating Einstein solutions to rotating solutions is a part of the thesis. This algorithm has been applied for obtaining rotating Myers-Perry black hole solution that have two rotational parameters. Using quaternions, we are able to find these solutions only in one step. The results of this thesis, can help us to understand black holes physics and explore their statistical microstates. In the end, it have been suggested some proposals continuing and completing these studies.