  We study the dynamics of one-particle and few-particle billiard systems in
containers of various shapes. In few-particle systems, the particles collide
elastically both against the boundary and against each other. In the
one-particle case, we investigate the formation and destruction of resonance
islands in (generalized) mushroom billiards, which are a recently discovered
class of Hamiltonian systems with mixed regular-chaotic dynamics. In the
few-particle case, we compare the dynamics in container geometries whose
counterpart one-particle billiards are integrable, chaotic, and mixed. One of
our findings is that two-, three-, and four-particle billiards confined to
containers with integrable one-particle counterparts inherit some integrals of
motion and exhibit a regular partition of phase space into ergodic components
of positive measure. Therefore, the shape of a container matters not only for
noninteracting particles but also for interacting particles.
