This volume includes twelve solicited articles which survey the current state of knowledge and some of the open questions on the mathematics of aperiodic order.

Quasicrystals: The State of the Art has proven to be a useful introduction to quasicrystals for mathematicians, physicists, materials scientists, and students.

This first-ever detailed account of quasicrystal geometry will be of great value to mathematicians at all levels with an interest in quasicrystals and geometry,

Quasicrystals form a new state of solid matter beside the crystalline and the amorphous. The positions of the atoms are ordered, but with noncrystallographic ro