After describing x-ray diffraction in Chap. 1 and electron diffraction in Chap. 2, Chap. 3 describes neutron diffraction and the other major methods of neutron scattering by materials. Sources of neutrons (nuclear reactors and accelerators) are described, as are key aspects of neutron powder diffractometers that are used at these different sources. A concept of diffraction, a wave of phase through a periodic material, is developed in anticipation of phase factors that are presented in Chap. 4. Other neutron instruments for measuring large-scale structures (reflectometers and small-angle scattering spectrometers) are discussed with this concept of a wave of phase, and moving phase waves are used to explain some aspects of inelastic neutron scattering. The chapter describes how neutrons are scattered by nuclei and by magnetic electron density.