  A role of the exterior differential forms in field theory is connected with a
fact that they reflect properties of the conservation laws. In field theory a
role of the closed exterior forms is well known. A condition of closure of the
form means that the closed form is the conservative quantity, and this
corresponds to the conservation laws for physical fields. In the present work a
role in field theory of the exterior forms, which correspond to the
conservation laws for the material systems is clarified. These forms are
defined on the accompanying nondifferentiable manifolds, and hense, they are
not closed. Transition from the forms, which correspond to the conservation
laws for the material systems, to those, which correspond to the conservation
laws for physical fields (it is possible under the degenerate transform),
describe a mechanism of origin of the physical structures that format physical
fields. In the work it is shown that the physical structures are generated by
the material systems in the evolutionary process. In Appendices we give an
analysis of the principles of thermodinamics and equations of the
electromagnetic field. A role of the conservation laws in formation of the
pseudometric and metric spaces is also shown.
