In this thesis, after reviewing concepts such as entanglement entropy in quantum field theories, correspondence of Anti-de Sitter space and conformal field theory (AdS/CFT) and holographic entanglement entropy, we investigate a method for calculating the holographic entanglement entropy of asymptotically AdS_3 space-time. Then, by extending this method to higher dimensions, we arrive at a general relation for calculating the entanglement entropy of asymptotically AdS_ {d + 1} black holes at the first order of the metric perturbation. Using this relation, We calculate the holographic entanglement entropy for the rotating cylindrical black holes in d+1 dimensions as perturbations over AdS_{d+1}. For these types of black holes, in addition to energy, the angular momentum also appears at the first order of the perturbative expansion of the holographic entanglement entropy. Therefore, by defining the entanglement temperature and the entanglement angular velocity, we write a relation similar to the first law of thermodynamics in the presence of both energy and angular momentum. In the last part of this thesis, we study a holographic extended phase space in the presence of Reier-Nordstrom-Anti-de Sitter and Born-Infeld-Anti-de Sitter black holes. In this extended phase space the cosmological constant is considered as pressure and volume related to the minimal area, appearing in the computation of the holographic entanglement entropy, which is the holographic dual of the complexity quantity, is defined as thermodynamic volume. our results show a Van der Waals-like structure for Reier-Nordstrom-Anti-de Sitter black holes in this extended phase space. For Born-Infeld-Anti-de Sitter black holes with a Born-Infeld parameter \\beta and charge Q, we observe the analogy with a Van der Waals liquid-gas system for \\beta Q 1/2 and Reentrant phase transition for \\beta Q 1/2 in the holographic extended phase space.