The first part covers the history of crystallography, the use of X-ray diffraction to study crystal structures through the Bragg peaks formed on their diffraction patterns, and the discovery in the early 1980s of quasicrystals, materials that form Bragg peaks in patterns with five-way symmetry, impossible for a repeating crystal structure.
Finally, it discusses a method for constructing Delone sets that have Bragg peaks by projecting bounded subsets of higher-dimensional lattices into lower-dimensional spaces.
[2] This material also has strong connections to spectral theory and ergodic theory, deep topics in pure mathematics, but these were omitted in order to make the book accessible to non-specialists in those topics.
)[1] The second part of the book discusses methods for generating these tilings, including projections of higher-dimensional lattices as well as recursive constructions with hierarchical structure, and it discusses the long-range patterns that can be shown to exist in tilings constructed in these ways.
Nevertheless, chemist István Hargittai writes that it can be read with interest by "students and researchers in mathematics, physics, materials science, and crystallography".