The task of modelling the evolution of cities - the dynamics - is one of the major challenges of the social sciences. This book presents mathematical and computer models of urban and regional dynamics and shows how advances in computer visualisation provide new insights. Models of non-linear systems in general have three characteristics: multiple equilibria, 'path dependence' over time and phase transitions - that is, abrupt change at critical parameter values. These phenomena all exhibit themselves in reality, and it is an ongoing task to match model-based analysis with real phenomena....