Aperiodic Order: Crystallography and Almost Periodicity

Quasicrystals are non-periodic solids that were discovered in 1982 by Dan
Shechtman, Nobel Laureate in Chemistry 2011. The mathematics that underlies this
discovery or was stimulated by it, which is known as the theory of Aperiodic Order,
is the subject of this comprehensive multi-volume series.
This second volume begins to develop the theory in more depth. A collection of
leading experts in the field, among them Robert V. Moody, introduce and review
important aspects of this rapidly-expanding field.
The volume covers various aspects of crystallography, generalising appropriately
from the classical case to the setting of aperiodically ordered structures. A strong
focus is placed upon almost periodicity, a central concept of crystallography that
captures the coherent repetition of local motifs or patterns, and its close links to
Fourier analysis, which is one of the main tools available to characterise such
structures. The book opens with a foreword by Jeffrey C. Lagarias on the wider
mathematical perspective and closes with an epilogue on the emergence of
quasicrystals from the point of view of physical sciences, written by Peter Kramer,
one of the founders of the field on the side of theoretical and mathematical physics.