  We present a theory of neutrino interactions with nuclei aimed at the
description of the partial cross-sections, namely quasi-elastic and
multi-nucleon emission, coherent and incoherent single pion production. For
this purpose, we use the theory of nuclear responses treated in the random
phase approximation, which allows a unified description of these channels. It
is particularly suited for the coherent pion production where collective
effects are important whereas they are moderate in the other channels. We also
study the evolution of the neutrino cross-sections with the mass number from
carbon to calcium. We compare our approach to the available neutrino
experimental data on carbon. We put a particular emphasis on the multi-nucleon
channel, which at present is not easily distinguishable from the quasi-elastic
events. This component turns out to be quite relevant for the interpretation of
experiments (K2K, MiniBooNE, SciBooNE). It can account in particular for the
unexpected behavior of the quasi-elastic cross-section.
