Minimizing an expectation gives little control of the risk of a reward that is far from the expected value. So, it is useful to design functionals whose minimization will allow one to make a tradeoff between the risk and expected value. This chapter gives a concise introduction to the corresponding theory of risk measures. After an introduction to utility functions, the monetary measures of risk are introduced and connected to their acceptation sets. Then the case of deviation and semi-deviation, as well as the (conditional) value at risk, are discussed.