Abstract. Probabilistic model checking is an automated verification method that aims to establish the correctness of probabilistic systems. Probability may arise, for example, due to failures of unreliable components, communication across lossy media, or through the use of randomisation in distributed protocols. Probabilistic model checking enables a range of exhaustive, quantitative analyses of properties such as "the probability of a message being delivered within 5ms is at least 0.89". In the last ten years, probabilistic model checking has been successfully applied to numerous real-world case studies, and is now a highly active field of research. This tutorial gives an introduction to probabilistic model checking, as well as presenting material on selected recent advances. The first half of the tutorial concerns two classical probabilistic models, discrete-time Markov chains and Markov decision processes, explaining the underlying theory and model checking algorithms for the temporal logic PCTL. The second half discusses two advanced topics: quantitative abstraction refinement and model checking for probabilistic timed automata. We also briefly summarise the functionality of the probabilistic model checker PRISM, the leading tool in the area.