This document is about the theoretical foundations of neoclassical consumer theory. In the first part, the document makes a presentation of the Arrow-Debreu model and presents the problem of maximization of utility and minimization of expenditure from the real approach (set theory). In the second part, it analyzes the problem of integrability. Then, in the third part, it analyzes the classification of the goods by their elasticities. In the fourth and last part, we made empirical applications of consumer theory.