The goal of the JDN22 school was to propose a progressive teaching eager to improve the expertise of students in neutron diffraction. Neutron-based techniques have indeed proved for decades to be essential tools in the investigation of condensed matter. This lecture is however concerned with inelastic neutron scattering and is thus somehow apart. In the context of this school, it should then only be considered as a brief introduction. We give simple examples along with the basics of the spectrometers, and finally useful formula for the inelastic cross sections in different situations. We strongly encourage interested readers to refer to the bibliography for more detailed information.