A general theory of discrete choice is developed around the notion of the existence of population choice behaviour defined in terms of a set of individual behaviour rules, and a structure of the utility function that contains a random utility component. Individuals are assumed to choose the alternative that yields the highest utility. For this reason, the empirical structure of the utility function is of central concern in individual choice modelling, and represents the mechanism by which the attributes of the alternatives and the individual socioeconomic environment influence the choice probabilities and hence the predictive capability of the model. To make the individual choice model operationally tractable, a number of axioms have been developed to condition the interpretation placed on the empirically identifiable selection probabilities. The chapter concludes with a simple example of the application of the basic choice model.