  In this Thesis we develop the geometric formulations for higher-order
autonomous and non-autonomous dynamical systems, and second-order field
theories. In all cases, the physical information of the system is given in
terms of a Lagrangian function/density, or a Hamiltonian that admits Lagrangian
counterpart. These geometric frameworks are used to study several relevant
physical examples and applications, such as the Hamilton-Jacobi theory for
higher-order mechanical systems, relativistic spin particles and deformation
problems in mechanics, and the Korteweg-de Vries equation and other systems in
field theory.
