This survey of the theory of mathematical billiards reflects the present state in this

very active research area. The author attempted to make the exposition as geometrical

as possible. Smooth convex billiards, billiards in polygons and polyhedra, and chaotic

dispersing billiards are treated in separate chapters. Another chapter concerns a lesser-known

topic of dual (or outer) billiards. The survey is intended for non-experts and

provides a general mathematical background for the study of billiards.