Understanding and controlling the physics of space charge effects in linear and circular proton and ion accelerators are essential to their operation, and to future high-intensity facilities. This book presents the status quo of this field from a theoretical perspective, compares analytical approaches with multi-particle computer simulations and - where available - with experiments. It discusses fundamental concepts of phase space motion, matched beams and modes of perturbation, along with mathematical models of analysis - from envelope to Vlasov-Poisson equations. The main emphasis is on...