  A perturbation theory scheme in terms of electron hopping, which is based on
the Wick theorem for Hubbard operators, is developed. Diagrammatic series
contain single-site vertices connected by hopping lines and it is shown that
for each vertex the problem splits into the subspaces with ``vacuum states''
determined by the diagonal Hubbard operators and only excitations around these
vacuum states are allowed. The rules to construct diagrams are proposed. In the
limit of infinite spatial dimensions the total auxiliary single-site problem
exactly splits into subspaces that allows to build an analytical
thermodynamically consistent approach for a Hubbard model. Some analytical
results are given for the simple approximations when the two-pole
(alloy-analogy solution) and four-pole (Hartree-Fock approximation) structure
for Green's function is obtained. Two poles describe contribution from the
Fermi-liquid component, which is dominant for small electron and hole
concentrations (``overdoped case'' of high-$T_c$'s), whereas other two describe
contribution from the non-Fermi liquid and are dominant close to half-filling
(``underdoped case'').
