The non - equilibrium theory of strongly correlated systems is proposed theory which is grounded on the generalized Wick theorem. This theorem is employed for calculation of the thermal averages of the contour arranged products of electron operators by generalizing Keldysh formalism. Perturbation expansion is realized for Anderson impurity model in which we consider the Coulomb interaction of the impurity electrons as a main parameter of the model and the mixing interaction between impurity and conduction electrons as a perturbation. The first two approximations are used for obtained the value of the current between one of the leads and central region of interacting electrons. The contribution of the strong correlations and of irreducible diagrams is analyzed.