Abstract
The technique of electron energy loss spectroscopy has provided us with a large body of data on the vibrational normal modes of atoms and molecules adsorbed on crystal surfaces, and of atoms within the outermost surface layers of crystals. In this paper, we review the theoretical description of the inelastic scattering events studied by the method, with emphasis on a series of recent calculations directed at a quantitative description of scattering events in which the electron emerges far from the specular direction or that of a Bragg beam , as a consequence of exciting a vibrational mode of short wavelength.