This text presents both a comprehensive framework for characterizing all forms of systems problems, and a set of specific methodologies for some key problems. These methodologies are based on a combination of classical and fuzzy set theories, probability and possibility theories, graph and hypergraph theories, and information theory, among others. The hardcopy text contains a revised, updated and condensed version of the first edition, accompanied by a CD containing supplementary material including additional chapters on related topics, explanatory material drawn from many years of class presentations and lectures, exercises, and fully worked out examples showing both the framework and methodology in operation on actual real-world problems. Fully operational software is made available on an associated website. The material is suitable for upper-level undergraduates and first-year graduate students with a modest background in discrete mathematics, probability and statistics.