**Justification**

Systems of the billiard type represent one of
the most popular and best investigated class of hyperbolic dynamical
systems. The billiard problem is a fascinating subject providing
a fertile source of new problems such as conjecture testing in
dynamics, geometry, theoretical and mathematical physics, mathematics,
optics, thermodynamics, spectral theory, etc. Thus, since the
early beginnings of the study of classical and quantum chaos,
billiards have been used as a paradigm.

Billiards correspond to one of the best understood
classes of dynamical systems that demonstrate a broad variety
of behaviours including passages from integrable to mixed form
and eventually to an entire chaotic dynamics. In fact, several
key properties of chaotic dynamics were first observed and demonstrated
for billiards. Many popular models of statistical mechanics, e.g.,
the Lorenz gas, the hard sphere (Boltzmann and Sinai) gas, etc.,
can be reduced to billiards. Moreover, examples of some formal
models of the billiard type exhibit a wide class of behaviours
with a number of new unexpected features. Such fundamental notions
as Boltzmann ergodic hypothesis, Fermi acceleration, Maxwell's
demon, Hamiltonian systems with divided phase space, the Riemann
zeta-function, etc. obtain natural physical realizations.

The aim of this school-conference is to bring
together renowned scientists in the field, leaving enough time
and opportunity for fruitful discussions among the participants.