Foundations of Crystallography with Computer Applications . Second edition. By Maureen Julian. CRC Press, 2015. Pp. 680. Price USD 84.96 (book and e‐book), USD 69.97 (e‐book). ISBN 978‐1‐4665‐5291‐3 .

The aim of this book is to describe the symmetry tools used to interpret crystal structures. The style of the book is striking: lengthy front matter (74 pp.), including a superfluous 28 pages of lists of tables and figures, lengthy chapter introductions with exhaustive lists of contents and ‘chapter objectives’, ample space to explain most simple ideas and verbose explanations for simple calculations while being terse when things become more complicated. The text is well understandable for beginners with no previous knowledge, with a clear didactic presentation. Numerous end-of-chapter exercises offer the possibility to apply the learned material; solutions to the problems are not offered either in the book or at the resources for the student on the book’s website. The first sentence of the Introduction reads ‘Crystallography is the science of finding the locations of atoms in crystals’. This definition is an inadmissible abridgement of what crystallography really is, what is even evident from the subjects dealt with in the book. The first five chapters (286 pp.) are devoted to fundamental crystallographic notions: lattices, crystallographic calculations like cell transformations and distance calculations using matrix algebra, reciprocal lattice, basics of group theory including subgroups and trees of group–subgroup relations, symmetry operations and their mathematical treatment, point groups and space groups. Worked-out examples amply explain symmetry as well as calculation procedures using numerical values from real crystal structures. Several basic crystallographic notions have not been included in these introductory chapters, but are postponed to Chapters 9 to 15, where they are explained in the context of some specific example; for example, fourfold screw axes are mentioned only briefly in Chapter 4, a more detailed explanation following in the context of the crystal structure of cristobalite in Chapter 12. All ideas are first developed in two dimensions, ‘for clarity and simplicity’. At the beginning, this is OK, but repeating this approach again and again in following chapters becomes tiring and is no longer helpful, taking into account that no real crystal occurs in two-dimensional space. Often the symmetry of a crystal structure is first described by stating the plane-group symbols of projections instead of commenting on the real structure in the first place. For example, Fig. 4.10b shows a structure drawn such that the reader rapidly realizes that it is centrosymmetric (in three dimensions) with atoms on two levels, but it is presented as having twofold rotational symmetry, which is only true for the projection but not for the structure; this unnecessarily complicates the description. It can be positively remarked that, generally, the book strictly observes the rules, symbols and standards of the International Tables for Crystallography, but there are some remarkable exceptions. For example, a mirror plane perpendicular to y is termed mx (in two dimensions) and mxz (in three dimensions) instead of my, which is confusing and not in accordance with the standards. Chapter 6 deals with X-rays and their diffraction, the emphasis being on theoretical relations and calculations. Aside from the generation of X-rays, experimental aspects are only of marginal interest; the Ewald construction to explain diffraction geometrically is missing. Chapter 7 explains the structure factor and the calculation of electron-density ISSN 2053-2733