  Volume or statistical averaging of the microscopic Maxwell equations (MEs),
i.e. transition from microscopic MEs to their macroscopic counterparts, is one
of the main steps in electrodynamics of materials. In spite of the fundamental
importance of the averaging procedure, it is quite rarely properly discussed in
university courses and respective books; up to now there is no established
consensus about how the averaging procedure has to be performed. In this paper
we show that there are some basic principles for the averaging procedure
(irrespective to what type of material is studied) which have to be satisfied.
Any homogenization model has to be consistent with the basic principles. In
case of absence of this correlation of a particular model with the basic
principles the model could not be accepted as a credible one. Another goal of
this paper is to establish the averaging procedure for metamaterials, which is
rather close to the case of compound materials but should include magnetic
response of the inclusions and their clusters. We start from the consideration
of bulk materials, which means in the vast majority of cases that we consider
propagation of an electromagnetic wave far from the interfaces, where the
eigenwave in the medium has been already formed and stabilized. A basic
structure for discussion about boundary conditions and layered metamaterials is
a subject of separate publication and will be done elsewhere.
