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 dominantes, 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.