]For the entire collection see Zbl 0714.00021] Introducing the notion of a diffiety and a spectral sequence over a diffiety, the author develops a new point of view for the theory of the characteristic classes. Through the prolongation, differential equations on a manifold are lifted into a diffiety, which may be considered as a manifold. Using the infinite order contact structure, called Cartan distribution, differential forms on a diffiety may be given a structure to form a spectral sequence in which the theory of the characteristic classes is embedded, in fact, the author reproduces the theory of characteristic classes and numbers in terms of special elements and their images in the spectral sequence. This point of view might help to understand a link between the formal geometry and the formal interpretation of physics.