Lecture on black hole perturbations by "Hugo Roussille"

These lectures will overlook black hole perturbation theory in GR, from its more fundamental aspects to its observational applications. After a presentation of the various motivations for the study of these perturbations, we will work out the Regge-Wheeler and Zerilli equations using metric perturbations. We will study the time-domain resolution of these equations, introducing quasi-normal modes and tails. We will then detail several quasi-normal modes computation techniques and link them to the context of the black hole spectroscopy program.