In this thesis black holes’ thermodynamics were investigated to obtain more information about critical behaviors and phase transitions for known black holes. Since the simplest known black hole is the Shwartzchild kind, we begin our discussion with this type in flat space. It will be shown that in flat space-time Shwartzchid black hole is unstable due to having negative heat capacity. But existence of electric charge and angular momentum will make it more stable. It can be observed that in Anti de- Sitter space-time, there is a phase transition for the shwartzchid kind from unstable black hole to stable black hole when we let the cosmological constant vary. we investigate critical behaviors and phase transition of RN and Kerr black holes in Anti de- Sitter space-time. In this case, we assume the cosmological constant as the thermodynamic pressure and introduce the conjugate quantity of the pressure as a thermodynamic volume. Also we expand our discussion to higher order gravities specially to Gauss-Bonnet and Lovelock gravity. We also take into account the non- linear effects of electrodynamics in our calculations.
