1. Introduction
2. Large-scale applications
3. Prototypical models
4. Fundamentals of probability, random processes, and statistics
5. Representation of random inputs
6. Parameter selection techniques
7. Frequentist techniques for parameter estimation
8. Bayesian techniques for parameter estimation
9. Uncertainty propagation in models
10. Stochastic spectral methods
11. Sparse grid quadrature and interpolation techniques
12. Prediction in the presence of model discrepancy
13. Surrogate models
14. Local sensitivity analysis
15. Global sensitivity analysis

The need to quantify and characterise uncertainties arising in mathematical models with unknown parameters leads to the rapidly evolving field of uncertainty quantification. This book provides readers with the concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models. It covers concepts from probability and statistics such as parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, and sensitivity analysis. The book goes on to explore applications and open problems from a wide array of disciplines, particularly those such as climate science, hydrology, and nuclear power where uncertainty quantification is crucial for both scientific understanding and public policy. An accompanying web page provides data used in the exercises and other supplementary material. The text is intended as a coursebook for advanced undergraduates and above, and as a resource for researchers in mathematics, statistics, operations research, science, and engineering.