The paper systemically describes the fundamental principle of the Green^,s function method. It demonstrates that the reversal relation holds only for the case of self-adjoint operator. The homogeneous boundary condition of the Green^,s function also comes from the self-adjointness of the differential operator while the Green integral formula does not directly apply to the non-self-adjoint operator. The paper also addresses perturbation expansion method induced by the Green^,s function, shows its relation to the popular Feynman diagram technique in physical science so as to help the student understanding the internal logics when learning advanced physics.