In this thesis, we investigate the critical behavior of Reier-Nordstrom, and its nonlinear generalization, Born-Infeld black holes in the AdS space in the framework of holography. We study phase structure of fidelity susceptibility and holographic complexity, which are given by maximal volume and the volume enclosed by minimal surface used to calculate holographic entanglement entropy. The critical behavior of AdS/RN in the extended phase space have been studied and its analogy with Van der Waals fluid have been shown. In this thesis, the phase structure of above-mentioned black holes, when the cosmological constant treated as a thermodynamic variable, will be studied holographicly
