Uncertainty quantification for hyperbolic and kinetic equations 1 The Stochastic Finite Volume Method 2 Uncertainty Modeling and Propagation in Linear Kinetic Equations 3 Numerical Methods for High Dimensional Kinetic Equations 4 From Uncertainty Propagation in Transport Equations to Kinetic Polynomials 5 Uncertainty Quantification for Kinetic Models in Socio Economic and Life Sciences 6 Uncertainty Quantification for Kinetic Equations 7 Monte Carlo Finite Volume Methods in Uncertainty Quantification for Hyperbolic Conservation Laws This book explores recent advances in uncertainty quantification for hyperbolic kinetic and related problems. The contributions address a range of different aspects including: polynomial chaos expansions perturbation methods multi level Monte Carlo methods importance sampling and moment methods. The interest in these topics is rapidly growing as their applications have now expanded to many areas in engineering physics biology and the social sciences. Accordingly the book provides the scientific community with a topical overview of the latest research efforts