The penetration of elecirons in solid matter is of considerable interest in many fields of applied physics. One application is found in Mössbauer spectroscopy, where spectra recorded by means of electrons are used for surface studies. This thesis deals with models for the penetration of medium fast electrons in solids, and with the electron transport and corresponding analysis involved in Mössbauer spectroscopical surface studies. Particular emphasis is given to the case where the electron energy loss is used to increase the analysing capability.