We have considered decision theory under certainty or for risk neutrality. we focus on the risk attitude of the agents. The model presented by von Neuman and Morgenstern allows to formalize risk aversion and risk loving. The objects of choice are lotteries, i.e., payoffs together with probabilities. We present and discuss the axioms that govern the choice between lotteries. We also introduce important concepts such as the certainty equivalent, the risk premium and the Arrow-Pratt measure of risk averseness.