In the first part of this thesis we study the entropy of black holes and in second part the effect of extra dimensions on structure of space-time and also compactefication and reduction of Einstein-Hilbert action investigated. Studding the space-time entropy is concentrated on 2D black holes and we will discuss about the effect of first quantum corrections on the thermo dynamical quantities. In second part we find how the compacted extra dimension on torus affect on general form of Einstein-Hilbert action in base space. Finally we analyze space time with two extra dimensions and consider the direct solutions of the reduced action. Key Words: General Relativity, Entropy, Dilaton, Torus, Reduction.