A self consistent gauge theory of Classical Lagrangian Mechanics, based on the introduction of the bundle ofaffine scalarsover the configuration manifold is proposed. In the resulting set-up, the “Lagrangian”Lis replaced by a section of a suitable principal fiber bundle over the velocity space, called the lagrangian bundle, while the associated Poincaré-Cartan 2-form is recognized as the curvature 2-form of a connection induced byLon a second “co-lagrangian” principal bundle. A parallel construction leads to the identification of a hamiltonian and a co-hamiltonian bundle over the phase space. An analysis of the properties of these spaces provides an intrinsic geometrical characterization of the Legendre transformation, thus allowing a systematic translation of the hamiltonian formalism into the newer scheme.