One common characteristic of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view of the topic. This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations on a variety of examples including the dynamics of bacterial biofilms, grassland savannahs, language competition and Internet social networking sites. The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new software tools for carrying out the necessary calculations. The book is intended for a general scientific audience of readers from the natural and social sciences, although it requires some mathematics to gain a full understanding of the more theoretical chapters. It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability.