Abstract: Discrete choice modelling has received a lot of attention these last decades. Indeed, forecasting human behavior in a choice context is very important in many fields, including marketing, economics, and transportation planning and operation. In the first part of the lecture, the basic theory of discrete choice models in general, and random utility theory in particular, will be introduced, motivated by some real applications. In the second part, we will focus on the estimation of such models, using real data. We will show that this task involves the maximization of a non linear objective function. Before describing an algorithm to solve this problem, we will analyze some theoretical properties of the objective function, related to its convexity and degeneracy.