The elastic scattering of electrons by the Coulomb potential of a nucleus is the most important of the interactions that contribute to image contrast. Cross-sections and mean-free-path lengths are used to describe the scattering process quantitatively. A knowledge of the screening of the Coulomb potential of the nuclei by the atomic electrons is important when calculating the crosssections at small scattering angles.The inelastic scattering is concentrated within smaller scattering angles and the excitation of energy states results in energy losses. The most important mechanisms are plasmon and interband excitations and inner-shell ionizations, which can be described by the dielectric theory. The inelastic scattering process is less localized than elastic scattering and cannot contribute to high resolution but the analytical modes of energy-loss spectroscopy become of greater interest. Inner-shell ionizations result in edge-shaped structures in the electron energy-loss spectrum (EELS), on which are superposed a near-edge structure (ELNES) and an extended energy-loss fine structure (EXELFS), which can be used for analytical electron microscopy at high spatial resolution.Even quite thin specimen layers, of the order of a few nanometres, do not show the angular or energy-loss distribution corresponding to a single scattering process. Multiple scattering effects have to be considered as the specimen thickness is increased and this can also result in electron-probe broadening.L. Reimer, Transmission Electron Microscopy