  Lagrangian submanifolds are becoming a very essential tool to generalize and
geometrically understand results and procedures in the area of mathematical
physics. Here we use general Lagrangian submanifolds to provide a geometric
version of the Hamilton-Jacobi equation. This interpretation allows us to study
some interesting applications of Hamilton-Jacobi equation in holonomic,
nonholonomic and time-dependent dynamics from a geometrical point of view.
