A high resolution energy-selecting electron beam apparatus and method for improving the energy resolution of electron-optical systems by restricting the energy range of admitted electrons, and optionally also for improving the spatial resolution by correcting chromatic and geometric aberrations. The apparatus comprises a plurality of magnetic or electrostatic prisms that disperse an electron beam according to the energies of the electrons into an energy spectrum, a plurality of magnifying lenses such as electromagnetic or electrostatic quadrupoles that increase the energy dispersion of the energy spectrum, an energy-selecting slit that selects a desirable range of energies of the electrons, and optionally also sextupole, octupole and higher-order lenses that correct chromatic and geometric aberration of the electron-optical system. The apparatus also comprises further magnetic or electrostatic prisms and electron lenses arranged such that the energy dispersion of the electron beam emerging from the apparatus is cancelled.