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This book provides an introduction and guide to modern advances in charged particle (and antiparticle) confinement by electromagnetic fields. Confinement in different trap geometries, the influence of trap imperfections, classical and quantum mechanical description of the trapped particle motion, different methods of ion cooling to low temperatures, and non-neutral plasma properties (including Coulomb crystals) are the main subjects. They form the basis of such applications of charged particle traps as high-resolution optical and microwave spectroscopy, mass spectrometry, atomic clocks, and, potentially, quantum computing. TOC:Introduction.- The Paul Trap.- The Penning Trap.- Other Traps.- Loading of Traps.- Trapped Charged Particle Detection.- Quantum States of Motion.- Coherent States for Dynamical Groups.- State Engineering and Reconstruction.- Trapped Ion Temperature.- Radiative Cooling.- Buffer Cooling.- Resistive Cooling.- Laser Cooling.- Adiabatic Cooling.- Trapped Non-Neutral Plasma.- Plasma Oscillations.- Coulomb Crystals.- Sympathetic Crystallization.- Appendices.