The Feynman-Dyson theory is extended so as to include the scattering involving composite particles. For this purpose we have clarified the relation of the Salpeter-Bethe wave functions to the probability amplitude by introducing co- and contra-variant components of state vectors keeping a close correspondence to the vector analysis in an oblique coordinate system. (§1). The integral equations for various kinds of Feynman kernels are derived in a systematic way by making use of functional differentiations with respect to external source, and these equations are shown to have formal solutions expressed in terms of Fermion kernels and various interaction operators. (§2) The procedure introduced by Gell-Mann and Low is fully utilized to derive integral equations for the covariant components with devices to suitably take account of the initial conditions. (§3) Finally the method to construct the S-matrix is discussed. (§4) Not discussed are the problems of renormalization and of metastable states.