We will briefly review some basic ideas of the Lagrangian and the Hamiltonian approach to classical field theory, including some examples. We will keep the talk at an elementary level (sometimes with a reduced level of mathematical rigor) and only indicate where more sophisticated concepts (e.g. jet bundles or infinite-dimensional manifolds) would enter the game. Some standard examples will be included.
This talk will serve as a sort of starting point of a series of talks/discussions of conserved charges in (super)gravity and related concepts.