In this book Thomas Saaty summarizes his Analytic Hierarchy Process (AHP) theory for measuring intangible factors through paired comparisons using judgments from which priorities are derived that give the relative dominance of these factors. The important concepts of the AHP and its generalization to structures with dependence and feedback, the Analytic Network Process (ANP), are presented in an elegant compact way and new extensions of the theory to complex decisions involving benefits, opportunities, costs and risks are presented. Applications to resource allocation and conflict resolution are included. The generalization to continuous comparisons is covered. The Encyclicon, three volumes are now available, is an encyclopedia of applications that is a useful accompaniment to the Principles of Mathematical Decision Making, containing of examples of practical decisions.