Textbook in PDF format Smith–Purcell radiation is the name given to the radiation produced when a charged particle beam, usually electrons, passes close to the surface of a metallic grating. The wavelength of the emitted radiation depends on the period of the grating and on the angle of observation. This makes this phenomenon a very useful tuneable source of radiation in the far-infrared (or THz) part of the spectrum, where tuneable sources are scarce. Moreover, a spectral analysis of the radiation can be used to reconstruct the time profile of the very short (picosecond or sub-picosecond) electron bunches that gave rise to this radiation. This is a parameter that is of interest to accelerator designers and users. The book is aimed primarily at experimentalists but starts with a relatively simple theoretical description of the origin of this radiation and then discusses its application either as a beam diagnostic tool or as a tuneable source of THz radiation. There is also a brief overview of other THz sources in order to allow the reader to assess the advantages of Smith–Purcell radiation