Originally written in 1964, this famous text is a study of the classical theory of charged particles. Many applications treat electrons as point particles. At the same time, there is a widespread belief that the theory of point particles is beset with various difficulties such as an infinite electrostatic self-energy, a rather doubtful equation of motion which admits physically meaningless solutions, violation of causality and others. The classical theory of charged particles has been largely ignored and has been left in an incomplete state since the discovery of quantum mechanics. Despite the great efforts of men such as Lorentz, Abraham, Poincare, and Dirac, it is usually regarded as a "lost cause". But thanks to progress made just a few years ago, the author is able to resolve the various problems and to complete this unfinished theory successfully.