Outer billiards is a dynamical system defined relative to a convex shape in the
plane. B. H. Neumann introduced outer billiards in the 1950s, and J. Moser popularized
the system in the 1970s as a toy model for celestial mechanics. When
the underlying shape is smooth, outer billiards has connections to area-preserving
twist maps and Kolmogorov-Arnold-Moser (KAM) theory. When the underlying
shape is a polygon, outer billiards is related to interval exchange transformations
and piecewise isometric actions. Outer billiards is an appealing dynamical system
because it is quite simple to define and yet gives rise to a rich intricate structure.