A few weeks ago, we attended a seminar by Eduardo Gracia Torano on Routh reduction in field theory. I am interested in revisiting the concept of Routh reduction, which originates from mechanics, and exploring the geometric structures that arise from it. In Hamiltonian mechanics with symmetry, it is customary to reduce the phase space without altering the Hamiltonian itself. However, Routh reduction, which is associated with the Lagrangian description of mechanics, involves reducing the entire Lagrangian bundle. This entails working with the space of infinitesimal configurations and the corresponding values of the Lagrangian, which often necessitates mathematical tools from the geometry of affine values.