  We present a detailed description of high-energy neutrino and antineutrino
inelastic inclusive scattering off nuclei in terms of nuclear structure
functions. In our approach we take into account a QCD description of the
nucleon structure functions as well as a number of basic nuclear effects
including nuclear shadowing, Fermi motion and binding, nuclear pion excess and
off-shell correction to bound nucleon structure functions. These effects prove
to be important in the studies of charged-lepton deep-inelastic scattering. We
discuss similarities and dissimilarities in the calculation of nuclear effects
for charged-lepton and neutrino scattering caused by nonconserved axial current
in neutrino scattering. We examine the Adler and the Gross-Llewellyn-Smith sum
rules for nuclear structure functions and find a remarkable cancellation
between nuclear shadowing and off-shell corrections in these sum rules. We
present calculations of differential cross sections for inclusive neutrino and
antineutrino scattering in comparison with recent data on different target
materials.
