The thesis is devoted to study modified theories of gravity. After a short review on the action and equations of motion of General Relativity and Friedman equations, f ( R; T ) theory is explained where T is the trace of energy momentum tensor and R is Richi scalar is explained. After obtaining equations of motion we study future singularities of two kinds of equations of state for this theory. We will see assuming conservation of energy and a constant equation of state parameter there is no future singularity but with changing equation of state it is possible to have some kinds of singularity which are categurized for this theory. Then we studied Neother symmetry for f ( R; T ) theory and calculated the conserved charge and Neother functions for two special cases. After that a short review on fundamentals of teleparallel gravity is presented which is an equivalent General Relativity with the difference that space-time is assumed to be twisted flat defined with Weitzenboch connection. Then f ( T ) theory is studied which is a straight forward modification of teleparalell gravity like f ( R ) theory for General Relativity. Then the method of dynamical systems is explained and three theories of gravity; f ( R; T ), f ( R; T;R __ T __ ) and f ( T ) is checked with this method. Critical points and phase trajectories are studied for these theories. We found f ( T ) and f ( R; T ) theories are able to explain the nowadays acceleration of the universe and some parts of standard cosmology. Finally mimetic theory is explained which is a solution to the problem of dark energy and dark matter. This theory is extended to explain f ( T ) mimetic dark matter.