Charged-particle optics enables us to study an extensive family ofdevices. At one extreme we have electron beams of low current densitytraversing static electron lenses, while at the other there are broad beamsin which the current density may be very high and the optic axis curved.D. Greenfield and M. Monastyrskiy have assembled here many of themathematical tools needed to study such situations; there is more empha-sis than in most of the related books on the charged-particle optics ofsystems in which the current density is significant and on time-dependentfocusing. In these respects, the present text complements those intendedfor students of electron optics