In this thesis we study the magnetic properties of materials in electron-electron interaction frame, by use of perturbation and retarded Green function and Anderson model. At first we suppose the host metal as a electron gas and ignore the correlation between electrons, because of spatial divergence of s-orbital. Then we add the impurity of d-orbital kind. in this stage we try to divide magnetic and non-magnetic regions by the mean field approximation, based on impurity and metal properties. We’ll see that there is a sharp transition between magnetic and non-magnetic region that depends on the density of free-electron states, the elements of s-orbital and d-orbital’s overlapping matrix or in a better word John-Tyler factors and also coulomb correlation integral in the interval d- orbital shell . The use of retarded green function and their equation of motions can help us to tackle this problem. We solve the equations, self consistently. Moreover we add f impurity to host metal and like above in low temperature obtain the magnetic of two impurities orbital. We try to compare the magnetic and non-magnetic phase with the change of properties of one impurity. The embedding of two magnetic atoms in normal metal leads to variety of interesting effects. Two different magnetic impurity coupled to the Fermi sea of the host metal, may lose or not its magnetic properties. In two different localized magnetic states d and f in metals the conditions necessary for the presence or absence of localized moments are analyzed. There is a special parameter that is the product of two John-Tyler factors ( gamma12 ) , and if it becomes zero, there would be no magnetization. a self consistent Hartree-Fock treatment for solute ions shows that there is a sharp and asymmetric transition between magnetic state and nonmagnetic state, depending on the density of states of free electrons, the s-d and s-f admixture matrix elements, and the Coulomb correlation integral in the d and f shell in the fact a preserved two localized magnetic moment coupled to the Fermi sea can lead to a correlated non-magnetic ground state of the whole system. At last numerical analyze of Anderson model for two different localized magnetic impurities indicates this fact that by addition of the certain impurity on a non-magnetic host metal, if we are able to add another kind to get a maximum magnetization or not. An answer to this question leads to find the process of magnetic change for different impurities. Observed correlations and symmetries in the graphs would help us to evaluate different impurities to reach the maximum magnetization. In a certain interval of energy there are some points that their md and mf are correlated i.e. both magnetization tend from maximum to minimum value Keywords: 1-Retarde Green functio 2-Anderson model 3-Mean field 4-John-Tyler 5-Equation of motion.