  These notes are a transcript of lectures given by the author in the XVIII
Modave summer school in mathematical physics. The introduction is devoted to a
detailed review of the literature on asymptotic symmetries, flat holography,
and the corner proposal. It covers much more material than needed, for it is
meant as a lamppost to help the reader in navigating the vast existing
literature. The notes then consist of three main parts. The first is devoted to
Noether's theorems and their underlying framework, the covariant phase space
formalism, with special focus on gauge theories. The surface-charges algebra is
shown to projectively represent the asymptotic symmetry algebra. Issues arising
in the gravitational case, such as conservation, finiteness, and integrability,
are addressed. In the second part, we introduce the geometric concept of
corners, and show the existence of a universal asymptotic symmetry group at
corners. A careful treatment of corner embeddings provides a resolution to the
issue of integrability, by extending the phase space. In the last part we
bridge asymptotic symmetries and corners by formulating the corner proposal. In
essence, the latter focuses on the central question of extracting from
classical gravity universal results that are expected to hold in the quantum
realm. After reviewing the coadjoint orbit method and Atiyah Lie algebroids, we
apply these concepts to the corner proposal. Exercises are solved in the notes,
to elucidate the arguments exposed.
