This is an introductory graduate-level course on uncertainty quantification and it is assumed that students have had undergraduate level training in statistics, linear algebra, and numerical methods for partial differential equations. The topics to be covered include: verification and validation of computational models, construction of probabilistic uncertainty models, Monte Carlo and Quasi-Monte Carlo simulation methods, importance sampling and variance reduction techniques, sparse quadrature schemes, perturbation methods, polynomial chaos expansions, stochastic Galerkin projection schemes, and an introduction to robust design optimization.