Abstract : A study is made of the general structure of all possible interpolation methods. For some applications intermediate spaces between two given Banach spaces for which such a general interpolation method exists are characterized. The relevant intermediate spaces are those which are called interpolation spaces between two given Banach spaces. The aim is to get rid of the redundant topoligical vector space in which the Banach spaces are usually supposed to be continuously imbedded. Further, normalized Banach subspaces of a given Banach space are introduced. The main theorem is that the lattice of these subspaces is complete and we give the construction of the joint and meet for an arbitrary class of such subspaces. The main results concerning interpolation methods and interpolation theorems are analyzed. (Author)