The deuteron stripping reactions are analyzed from the point of view of the many-body problem. A rigorous formal solution is given. From this it is shown how assumptions less restricted than Butler's can be employed to reduce the many-body interactions to those of a deuteron moving in a potential well. At this point, the relation to previous theories is readily established. The present theory might be termed "the optical model" of the stripping reactions and represents a considerable generalization of current theories.