  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 bulk MM, which is rather
close to the case of compound materials but should include magnetic response of
the inclusions and their clusters. In the vast majority of cases the
consideration of bulk materials means that we consider propagation of an
electromagnetic wave far from the interfaces, where the eigenwave in the medium
has been already formed and stabilized. In other words, in this paper we
consider the possible eigenmodes, which could exist in the equivalent
homogenized media, and the necessary math apparatus for an adequate description
of these waves. A discussion about boundary conditions and layered MM is a
subject of separate publication and will be done elsewhere.
