In this Lecture we discuss neutron scatteringScatteringneutron scattering on crystals. We calculate the lattice sumsLattice sumSumlattice sum considering both coherent and incoherent scatteringScatteringincoherent scattering processes. We evaluate the cross sections for elastic and inelastic (one-phonon) processes in mono- and polycrystals. We show inter-connection of the peaks of the doubly differential cross sectionCross sectiondoubly differential cross section for the inelastic processesProcessinelastic process with the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum.