  The general theory of neutron scattering is presented, valid for the whole
domain of slow neutrons from thermal to ultracold. Particular attention is
given to multiple scattering which is the dominant process for ultracold
neutrons (UCN). For thermal and cold neutrons, when the multiple scattering in
the target can be neglected, the cross section is reduced to the known value. A
new expression for inelastic scattering cross section for UCN is proposed.
Dynamical processes in the target are taken into account and their influence on
inelastic scattering of UCN is analyzed.
