Over the last quarter of this century, revolutionary advances have been made both in kind and in precision in the application of particle traps to the study of thephysics of charged particles, leading to intensified interest in, and wide proliferation of, this topic. This book is intended as a timely addition to the literature, providing a systematic unified treatment of the subject, from the point of view of the application of these devices to fundamental atomic and particle physics. The technique of using electromagnetic fields on fine and isolate atomic particles in vacuo, rather than by material walls of a container, was initially conceived by W.Paul in the form of a 3Dversion of the original rf quadrupole mass filter, for which he shared the 1989 Nobel Prize in physics [1], whereas H.G. Dehmelt who also shared the 1989 Nobel Prize [2] saw these devices (including the Penning trap) as a way of isolating electrons and ions, for the purposes of high resolution spectroscopy. These two broad areas of appli- tion have developed more or less independently, each attaining a remarkable degree of sophistication and generating widespread interest and experimental activity.