The theory of Markov decision processes focuses on controlled Markov chains in discrete time. The authors establish the theory for general state and action spaces and simultaneously show its application through numerous examples, mostly taken from the fields of finance and operations research. By using a structural approach, many technicalities concerning measure theory are avoided. They cover problems with finite and infinite horizons, as well as partially observable Markov decision processes, piecewise deterministic Markov decision processes, and stopping problems. The book presents Markov decision processes in action and includes various state-of-the-art applications with a particular emphasis on finance. It is useful for upper-level undergraduates, Master's students, and researchers in both applied probability and finance, and provides exercises without solutions.