Convexity is a central property for ensuring tractability in optimization problems and the uniqueness of the obtained solutions. This chapter elaborates on the significance of convex sets and functions in economic modeling. It discusses how diminishing marginal rates of substitution in consumer theory and of technical substitution in the theory of the firm translate into convex preferences and production sets. The key properties of convex programming problems are outlined, including the existence, uniqueness, and global nature of optima. Finally, the concept of duality is introduced and an economic interpretation of duality in convex programming is provided.