Studying of strongly correlated systems has been one of the most active subjects in solid state physics for past two decades. One of the most important subjects in this field is metal-insulator phase transition and why some of the materials are conductive and some are not. From the experimental point of view, if the temperature approaches zero and the conductivity of the material approaches zero, this material is assumed as insulator. There are three standard models for describing materials: 1) Band theory, 2) Mott insulator and 3) Anderson insulator. Investigating the effect of simultaneously strong interaction systems in presence of disorder (combination of Mott and Anderson insulator) is the purpose of the thesis. In this thesis, we investigate the Hubbardd model for strongly correlated system in presence of disorder in the atomic limit, ( u t ) by using the Hubbard-Stratonovich transform for a lattice in d dimensions. We formulate the role of disorder in these systems with u parameter. First we study the strongly correlated systems by creating the auxiliary Fermions and Hubbard-Stratonovich transform, then based on auxiliary Fermions we rewrite the Hamiltonian of systems, therefore, we can investigate the strongly correlated systems with the method of weak interaction systems and Wick theory. For this purpose different orders of cumulant are generated that we use Hubbard operators and Wick’s theorem and calculate the second and third cumulants for parallel spin then finally we will study the effect of disorder on these cumulants. Key Words: Strongly correlated system, Hubbard model, Hubbard-Stratonovich transform, Wick theorem, auxiliary Fermions, Hubbard operators, Wick theorem for Hubbard operators, Wick theorem for Hubbard operators, disorder parameter, Second Cumulant for parallel spin and anti parallel spin, third Cumulant for parallel spin and anti parallel spin.