The goal of this chapter is to provide a general introduction to decision making under uncertainty. The mathematical foundations of the most popular models used in artificial intelligence are described, notably the Expected Utility model (EU), but also new decision making models, like Rank Dependent Utility (RDU), which significantly extend the descriptive power of EU. Decision making under uncertainty naturally involves risks when decisions are made. The notion of risk is formalized as well as the attitude of agents w.r.t. risk. For this purpose, probabilities are often exploited to model uncertainties. But there exist situations in which agents do not have sufficient knowledge or data available to determine these probability distributions. In this case, more general models of uncertainty are needed and this chapter describes some of them, notably belief functions. Finally, in most artificial intelligence problems, sequences of decisions need be made and, to get an optimal sequence, decisions must not be considered separately but as a whole. We thus study at the end of this chapter models of sequential decision making under uncertainty, notably the most widely used graphical models.