In this chapter we introduce and study in some detail the notion of Lagrangian fibration with smooth fibers (Lagrangian fibration from now on) which is the differential geometrical counterpart of the notion of classical integrable system introduced in Chap. 1 . A particular emphasis will be given to the case of fibrations with compact, connected, and smooth fibers. For these fibrations, we prove the existence of the so-called action-angle coordinates, symplectic coordinates defined on a suitable tubular neighborhood of each fiber.