This is the proceedings of the fourth school in a series of specialized courses organized by CERN's CAS and the American USPAS. It deals with intensity limitations. The contribution thoroughly edited for this publication fall into the following categories: self and environmental fields - coherent instabilities and their simulation - beam-beam interaction - other multi-particle effects - beam source limitations - engineering limitations. This exposition of the inner working of high-intensity particle beams addresses particle physicistsas well as those that commission new machines. The...