Billiard Dynamics: An Updated Survey with the Emphasis on Open Problems

This is an updated and expanded version of our earlier survey article \cite{Gut5}. Section $§1$ introduces the subject matter. Sections $§2 - §4$ expose the basic material following the paradigm of elliptic, hyperbolic and parabolic billiard dynamics. In section $§5$ we report on the recent work pertaining to the problems and conjectures exposed in the survey \cite{Gut5}. Besides, in section $§5$ we formulate a few additional problems and conjectures. The bibliography has been updated and considerably expanded.

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