  We develop a general theory of a boson decomposition for both local and
non-local interactions in lattice fermion models which allows us to describe
fermionic degrees of freedom and collective charge and spin excitations on
equal footing. An efficient perturbation theory in the interaction of the
fermionic and the bosonic degrees of freedom is constructed in so-called dual
variables in the path-integral formalism. This theory takes into account all
local correlations of fermions and collective bosonic modes and interpolates
between itinerant and localized regimes of electrons in solids. The zero-order
approximation of this theory corresponds to extended dynamical mean-field
theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is
provided. It is shown that dual ladder summation gives a conserving
approximation beyond EDMFT. The method is especially suitable for consideration
of collective magnetic and charge excitations and allows to calculate their
renormalization with respect to "bare" RPA-like characteristics. General
expression for the plasmonic dispersion in correlated media is obtained. As an
illustration it is shown that effective superexchange interactions in the
half-filled Hubbard model can be derived within the dual-ladder approximation.
