Introduction to Crystallography . By Frank Hoffmann. Springer, 2020. Hardback, pp. x+309. Price GBP 59.99. ISBN 9783030351090.

to Crystallography by Frank Hoffmann is the English version of a German textbook (Hoffmann, 2016). It consists of nine chapters and three appendices, followed by a detailed index spanning three pages. About two-thirds of the content (the first six chapters) is devoted to crystal symmetry, and the other third to the description of some crystal structures, aperiodic crystals and some notions of reticular chemistry. The original title (The Fascination of Crystals and Symmetry) is somewhat more loyal to the content of the book. Indeed, the more formal English title Introduction to Crystallography might suggest content in the lineage of classical textbooks like Buerger’s (1956) book, for example. Instead, Hoffmann’s textbook systematically avoids every possible obstacle for the student less inclined to abstract thinking and mathematical descriptions, giving instead priority to an intuitive pictorial approach. It can be described as a ‘how to’ manual for an end user with insufficient basic knowledge to pretend accessing a more formal description (‘we do not want to deal with group theory here’, p. 94). Students of the earth sciences seem to be the natural target, but those enrolled in chemistry will also most likely enjoy this book. Life scientists could also profit from the simplicity of the presentation, although they will miss examples close to their field. Students of physics, on the other hand, will clearly be highly dissatisfied by the complete lack of formal descriptions (no metric tensor, no matrices, no calculations at all). Once we accept the absence of any formal approach to the subject, the book stands out from many concurrent, even much more pretentious, works for its rigour of language (with some exceptions discussed below) which, although unable to reach perfection, is certainly higher than that in most of the books published in recent years. Moreover, the book comes with an online resource depository companion, where the reader finds paper models for the 32 (geometric) crystal classes, short videos showing animations of the actions of glide planes and screw axes whose static versions are published in the book, and CIF files of crystal structures presented in the text. Chapter 1 (32 pages) is humbly entitled Introduction. Contrary to so many textbooks that present a dry and unappetizing approach to the basic definitions, it provides an unusual but tasty ‘first bite’ of the subject. It starts with a comparison of the sizes of objects differing by powers of 10 (reference to the well known short movie acknowledged) to introduce the notion of crystal structure in a very intuitive way. This is followed by a crystallographic poem summarizing some crystallographic terms that might sound cryptic to the beginner, and a graphic backbone using the words ‘crystal’ and ‘lattice’ taken from the well known book by the Canadian poet Christian Bök (2003). At this point, the reader is, one hopes, hooked by the fascinating beginning of the narration, which goes on to emphasize the difference between a structure and its lattice, through examples of periodic (as well as some counter-examples of non-periodic) arrangements of objects (tuna tins, bags of crisps, cola cans). Knowing how severe is the confusion between structure and lattice even in the mind of confirmed scientists (Nespolo, 2019), the efforts made to prevent any possible such confusion in the mind of the new reader is extremely welcome. The second part of the chapter goes back to a more traditional description and introduces the notions of unit cell and crystal system. Most welcome is the emphasis put on the restrictions imposed on the cell parameters by symmetry and the incorrect way most textbooks present them (Tables 1.1 and 1.2), something I have long been pestering about without much success (Nespolo, 2015). The three examples on ISSN 2053-2733