The Ammann-Beenker tiling is the eight-fold sibling of the more famous, five-fold Penrose rhomb tiling. It was discovered independently by R. Ammann [AGS92] and F. Beenker [Bee82]. It shares many properties with the Penrose tiling. In particular it shares two particular constructions. The first by a substitution rule, and the second as a slice of a higher dimensional lattice. Also it shares the important property with the Penrose that it is a strikingly beautiful tiling.