Almost everything that is interesting and important for society is complex; here, examples scattered across the sciences are presented in order to illustrate the cross-disciplinary richness of state-of-the-art complex systems research: fracture avalanches and rain showers that mimic earthquakes; highly organized graphs that account for processes in neural networks, metabolic networks, food webs, or language; models for DNA dynamics; or statistical methods to test complexity in the form of structure on many different scales. In this context, mathematics is put to work to model the real system, and the models are kept at a minimum level so as not to interfere with understanding the essentials of the real system.

The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.