Solutions of the field equations for the some extended theories of gravity by the symmetry approach

Einstein's general theory of gravitation is the best theory of describing the development and evolution of the present universe. Nevertheless, it is insufficient to explain some of the new observations. Thus, some new theories of gravity have emerged, that gives the theory of Einstein's GRT in the case of limit, to explain new observations. In this thesis, firstly the f(R) theory of gravity will be studied in the framework some sort of space-times such as spherical symmetric, cylindrically symmetric, and plane symmetric space-time. Then, the minimally coupled scalar tensor theory of gravity will be considered in the framework LRS Bianchi type I space-time. In each case, universe models will be constructed and Noether symmetry approach will be used to find exact solutions.