This preprint contains proofs of the results anounced in Panin-Smirnov in the part concerning the construction of push-forwards for an oriented cohomology theory. It is constructed one-to-one correspondences between orientations, Chern structures, Thom structures and integrations on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples.