In optimal control theory, Pontryagin’s maximum principle is a set of necessary conditions that generalizes Euler-Lagrange equation in the classical calculus of variations to cases where the trajectory is subject to additional constraints. The problem can be cast in an abstract framework as constrained optimization in metric spaces. This thesis introduces this formulation and shows that the maximum principle can be obtained in a familiar way as (similar to Kuhn-Tucker's for R^n) necessary conditions in constrained optimization.