Hydrologic systems are both complex and extremely heterogeneous in time and space. As hydrological models are simplified versions of reality, their predictions are by definition subject to uncertainty. The field of stochastic hydrology focuses on quantifying this uncertainty along with prediction. This book aims to present an overview of the field of stochastic hydrology at an introductory level. A wide range of topics and methods will be treated, while each topic and method is only treated at a basic level: descriptive statistics; probability and random variables; hydrological statistics and extremes; random functions; time series analysis; geostatistics; forward stochastic modeling; and state prediction and Kalman filtering. The book can be used for a 10-15-week course at third-year undergraduate or first-year graduate level.