organize the published work in a uni?ed volume that de?nes the current status of the ?eld. As explained in volume I, the technique of con?ning charged particles in suitable electromagnetic ?elds was initially conceived by W. Paul as a thr- dimensional version of his rf quadrupole mass ?lter. Its ?rst application to rf spectroscopy on atomic ions was completed in H. G. Dehmelt¿s laboratory where notable work was later done on the free electron using the Penning trap. The further exploitation of these devices has followed more or less - dependently along the two initial broad areas: mass spectrometry and high resolution spectroscopy. In volume I a detailed account is given of the theory of operation and experimental techniques of the various forms of Paul and Penning ion traps.