Quantum Potential Theory Potential Theory in Classical Probability to Random Walks on Noncommutative Spaces Interactions between Quantum Probability and Operator Space Theory Dirichlet Forms on Noncommutative Spaces Applications of Quantum Stochastic Processes in Quantum Optics Quantum Walks. This volume contains the revised and completed notes of lectures given at the school Quantum Potential Theory: Structure and Applications to Physics held at the Alfried Krupp Wissenschaftskolleg in Greifswald from February 26 to March 10 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory concentrating on probabilistic potential theory and it quantum analogs i.e. quantum Markov processes and semigroups quantum random walks Dirichlet forms on C* and von Neumann algebras and boundary theory. Applications to quantum physics in particular the filtering problem in quantum optics are also presented.