Cornering Quantum Gravity

These lecture notes cover materials exposed by Luca Ciambelli at the 59 Winter School of Theoretical Physics and third COST Action CA18108 Training School "Gravity -- Classical, Quantum and Phenomenology", held in Palac Wojan\'ow, Poland, 12-21 Feb 2023. After introducing the covariant phase space calculus, Noether's theorems are discussed, with particular emphasis on Noether's second theorem and the role of gauge symmetries. This is followed by the enunciation of the theory of asymptotic symmetries, and later its application to gravity. Specifically, we review how the BMS group arises as the asymptotic symmetry group of gravity at null infinity. Symmetries are so powerful and constraining that memory effects and soft theorems can be derived from them. The lectures end with more recent developments in the field: the corner proposal as a unified paradigm for symmetries in gravity, the extended phase space as a resolution to the problem of charge integrability, and eventually the implications of the corner proposal on quantum gravity.