Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. The second edition is a significant expansion over the first one which meanwhile has become a standard reference in complex-system research and teaching. For example, probability concepts are presented more in-depth and the sections on Levy laws and the mechanisms for power laws have been greatly enlarged. Also, considerable material has been added to the chapter on renormalization-group ideas. Further improvements can be found in the applications to earthquake or rupture models. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in physics, ecophysics, geophysics and meteorology.