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This is the proceedings of the fourth school in a series ofspecialized courses organized by CERN's CAS and the AmericanUSPAS. It deals with intensity limitations. The contributionthoroughly edited for this publication fall into thefollowing categories: self and environmental fields -coherent instabilities and their simulation - beam-beaminteraction - other multi-particle effects - beam sourcelimitations - engineering limitations.This exposition of the inner working of high-intensityparticle beams addresses particle physicistsas well asthose that commission new machines. The lecturers werechosenas being at the forefront of latest developments inthis field.