  This manuscript contains the lecture notes of the short courses given by one
of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics
XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer
school "Glassy Systems and Inter-Disciplinary Applications", held in Cargese,
France, in June 2021. The course was a short introductory overview of the
dynamics of disordered systems, focused in particular on the equilibrium
dynamics (with the associated glass transition), and on the simplest case of
off-equilibrium dynamics, namely the gradient descent dynamics. A few selected
topics (and references) are chosen, based on the authors' own taste and
competences, and on pedagogical reasons, without aiming at a complete review of
the subject.
