  At present the theory of skew-symmetric exterior differential forms has been
developed. The closed exterior forms possess the invariant properties that are
of great importance. The operators of the exterior form theory lie at the basis
of the differential and integral operators of the field theory. However, the
theory of exterior forms, being invariant one, does not answer the questions
related to the evolutionary processes. In the work the readers are introduced
to the skew-symmetric differential forms that possess evolutionary properties.
They were called evolutionary ones. The radical distinction between the
evolutionary forms and the exterior ones consists in the fact that the exterior
forms are defined on manifolds with closed metric forms, whereas the
evolutionary forms are defined on manifolds with unclosed metric forms. The
mathematical apparatus of exterior and evolutionary forms allows description of
discrete transitions, quantum steps, evolutionary processes, generation of
various structures. These are radically new possibilities of the mathematical
physics. A role of exterior and evolutionary forms in the mathematical physics
is conditioned by the fact that they reflect properties of the conservation
laws and allow elucidate a mechanism of evolutionary processes in material
media, which lead to formatting physical fields.
