Ongoing global changes bring fundamentally new scientific problems requiring new concepts and tools. A key issue concerns a vast variety of practically irreducible uncertainties, which challenge our traditional models and require new concepts and analytical tools. The uncertainty critically dominates, e.g., the climate change debates. In short, the dilemma is concerned with enormous costs vs. massive uncertainties of potential extreme impacts. Traditional scientific approaches usually rely on real observations and experiments. Yet no sufficient observations exist for new problems, and "pure" experiments and learning by doing may be very expensive, dangerous, or simply impossible. In addition, available historical observations are contaminated by actions, policies. The complexity of new problems does not allow to achieve enough certainty by increasing the resolution of models or by bringing in more links. Hence, new tools for modeling and management of uncertainty are needed, as given in this book which was prepared for an interdisciplinary audience, and addresses open problems, limitations of known approaches, novel methods and techniques, or lessons from the applications of various approaches. Thus, the book contributes to a better understanding between practitioners dealing with the management of uncertainty, and scientists working on either corresponding modeling approaches that can be applied for improving understanding or management of uncertainty.