  Stability is one of the most fundamental aspects regarding planetary systems.
It plays an important role in our understanding on the formation channel of the
planetary systems, as well as their habitability. Many approaches have been
adopted to determine the stability of these systems, including brute-force
N-body simulations, semi-analytical calculations, and more recently machine
learning methods. This allows significant advances in our understanding of
planetary system dynamics, as well as providing tools to constrain unknown
parameters of exoplanetary systems (assuming these systems are stable). In the
following, we focus on planets around single star hosts, and we provide an
overview of the studies of planetary system stability for compact multi-planet
systems and hierarchical multi-planet systems.
