This course explores the theoretical foundations and applications of probabilistic modal logics. In the theoretical component, we will introduce propositional probability logic along with its infinitary extension. We will cover key concepts and techniques, including axiomatic systems, selected soundness and completeness results, decidability, and model-theoretic properties. In the applied component, we turn to probabilistic temporal logic and dynamic probability logic as formal systems for describing and reasoning about random dynamical systems. For this course, familiarity with the basic concepts of mathematical logic is required. Some knowledge of basic modal logic may be helpful, but is not essential.