This book combines coalgebraic reasoning, shastic systems and logics. It provides an insight into the principles of coalgebraic logic from a categorical point of view, and applies these systems to interpretations of shastic coalgebraic logics, which include well-known modal logics and continuous time branching logics. The author introduces shastic systems together with their probabilistic and categorical foundations and gives a comprehensive discussion of the Giry monad as the underlying categorical construction, presenting many new, hitherto unpublished results. He discusses modal logics, introduces their probabilistic interpretations, and then proceeds to an analysis of Kripke models for coalgebraic logics. The book will be of interest to researchers in theoretical computer science, logic and category theory.