Classical consumer theory is essentially the theory of utility maximization under a budget constraint. This theory starts with the definition of consumers' preferences. In classical consumer theory, preferences are assumed to be transitive, complete, monotone, and convex. These preferences can then be represented by utility functions. The latter are mathematically easier to handle than preferences. Another reason for being interested in utility functions goes back to the early phases of economic theory. Then, it was thought that utility functions could be used as a measure of consumer's satisfaction or utility. This chapter is devoted to a presentation of the basic issues regarding preferences and their representability by utility functions.