This is a corrected and expanded second edition of the author’s primer of 1992 — and, fortunately, it is still an introductory text. The author develops the theory of quasicrystals from the physical point of view, with quite some effort put on the relation to experiment. Topics include crystallography versus quasi-crystallography, connection to “real” quasicrystals, atomic models, perfect versus disordered structures, lattice dynamics and dislocations, and — finally — a decent chapter on relevant open questions.
Though this book is primarily written for physicists, crystallographers and material scientists it is certainly a very good reference also for mathematicians. Many of the questions addressed are mathematical, and the extensive lists of references (following every chapter) will be useful for further reading and research: due to the origin of the field, many fundamental results are published in physics journals, and not always easy to find.