It is shown that the equations of mathematical physics possess invariant properties. And this discloses a connection between the field-theory equations and the equations of mathematical physics. This connection enables to understand the basic principles of field theory and the connection between physical fields and material media. The field-theory equations are connected with the equations of mathematical physics, which describe material media (material systems). The equations of conservation laws for energy, linear momentum, angular momentum, and mass, which describe such material systems as the thermodynamic, gas-dynamic and cosmic systems, as well as the systems of charged particles and others, are precisely such equations of mathematical physics.