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This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present second volume contains the following lectures: "Random Walks on Finite Quantum Groups" by Uwe Franz and Rolf Gohm, "Quantum Markov Processes and Applications in Physics" by Burkhard Kümmerer, Classical and Free Infinite Divisibility and Lévy Processes" by Ole E. Barndorff-Nielsen, Steen Thorbjornsen, and "Lévy Processes on Quantum Groups and Dual Groups" by Uwe Franz.

Mathematics. --- Distribution (Probability theory). --- Mathematical physics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Mathematical and Computational Physics. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical Theory --- Physical mathematics --- Physics --- Distribution functions --- Frequency distribution --- Math --- Applied mathematics. --- Engineering mathematics. --- Probabilities. --- Physics. --- Theoretical, Mathematical and Computational Physics. --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Mathematical analysis --- Distribution (Probability theory. --- Characteristic functions --- Probabilities --- Stochastic analysis. --- Probabilistic number theory. --- Lévy processes. --- Random walks (Mathematics) --- Number theory --- Analysis, Stochastic --- Stochastic processes --- Distribution (Probability theory) --- Probability Theory.