  The paper continues a series of papers devoted to treatment of the
crystalline state on the basis of the approach in equilibrium statistical
mechanics proposed earlier by the author. This paper is concerned with
elaboration of a mathematical apparatus in the approach for studying
second-order phase transitions, both commensurate and incommensurate, and
properties of emerging phases. It is shown that the preliminary symmetry
analysis for a concrete crystal can be performed analogously with the one in
the Landau theory of phase transitions. After the analysis one is able to
deduce a set of equations that describe the emerging phases and corresponding
phase transitions. The treatment of an incommensurate phase is substantially
complicated because the symmetry of the phase cannot be described in terms of
customary space groups. For this reason, a strategy of representing the
incommensurate phase as the limit of a sequence of long-period commensurate
phases whose period tends to infinity is worked out. The strategy enables one
to obviate difficulties due to the devil's staircase that occurs in this
situation.
