International tables for crystallography. Vol. A. 5th edition. Edited by Th. Hahn. Pp. xx + 911. Dordrecht: Kluwer Academic Publishers, 2002. Price EUR 242, GBP 142, USD 225. ISBN 0‐7923‐6590‐9.

Since its ®rst appearance in 1983, Volume A of International Tables for Crystallography (hereafter ITA) has served `consumers' of symmetry-group data for about 20 years and has experienced, during a permanent dialog with the readers, four more or less major revisions. ITA is the ®rst in a series of International Tables for Crystallography and treats one-, twoand three-dimensional crystallographic space groups. Extensions to `generalized symmetry' are beyond the scope of this volume. A salient point of ITA is the adoption of an advanced level of symmetry theory, which is strictly compatible with the demands of computerization of crystallographic problems. The Editor's goal to provide data that are useful for all aspects of crystallography as well as text to satisfy the needs of those interested in the theoretical reasons behind these tables has led to a fruitful combination of tables for practical use in the ®rst part and a high-level textbook in the second. ITA succeeded in proposing a compromise between competing view points. I mention issues such as the hexagonal/trigonal versus rhombohedral subdivision and the so-called `monoclinic monster', which, for the convenience of the reader, is a summary of all settings and cell choices of the monoclinic space groups. Because symmetry is the basis of crystallography, previous editions of ITA had to be reissued several times: 1st edition 1983, reprinted with corrections 1984, 2nd revised edition 1987, 2nd revised edition reprinted with corrections 1989, 3rd revised edition 1992, 4th revised edition 1995, 4th revised edition reprinted with corrections 1996, 4th edition reprinted 1998, 5th revised edition 2002. The volume has increased from xv + 854 pages in 1983 to xx + 911 pages in 2002. This 5th edition (ITA5) is more extensively revised than any of the preceding editions. While the number of parts (15) is maintained in ITA5, the number of authors has increased. The ®rst edition of ITA was reviewed by Stadnicka et al. [Acta Cryst. (1987), A43, 156±159]. They concluded, after assessing all sections individually, that ITA is a clearly, thoroughly and coherently written book that has been prepared carefully and is of good technical quality. The reader of ITA5 will ®rst notice a new white (red)-green hard cover differing from the blue (gold) predecessors, this time without a book jacket. Although it looks more attractive at ®rst glance, the white part might lose its beauty more quickly. Then, looking at the layout of the interior, a smaller font attracts the reader's attention which makes the arrangement of the text more concise, because the number of lines per page is approximately maintained. Hence, more space between the subsections along with an in-depth four-digit decimal classi®cation facilitates browsing ITA5 considerably. The table of contents now covers 6 pages instead of 4 of the previous edition. The plain rearrangement of the text of the fourth edition is a noteworthy achievement of ITA5 in itself. One component of that is bringing tables or ®gures closer to the place where they are quoted ®rst. Moreover, instead of the creamy paper previously utilized, for the current edition white paper has been used. Again this makes reading easier, apart from proper fractions which, due to the smaller font, appear a bit faint now. However, the general quality of print is excellent. Then a hidden change in ITA5 should be mentioned, which will certainly become a great advantage for future application compared to editions 1±4. It is the computerbased production of ITA5, accomplished by M. I. Aroyo and P. B. Konstantinov. All space-group tables were reprogrammed, whereas the space-group diagrams were scanned from the existing presentations, which in turn had been improved several times over the years. One promising future option of this computerization is the linking of ITA5 to other volumes of this series. Because ITA is published for the International Union of Crystallography (IUCr), its content has been the subject of permanent attention by Commissions of the IUCr, in particular by the Commission on International Tables and the Commission on Nomenclature. Hence, unlike common texts or tables, ITA is being continuously improved by a well organized and competent community, whose recommendations, after thorough discussion, are taken as input for subsequent editions. One example was an inconsistency in the concept of `symmetry element' [H. D. Flack et al. (2000). Acta Cryst. A56, 96±98], which has been removed by de®ning the geometric element as a labelled geometric item. Hence corrigenda and addenda became necessary. Those of the third edition were summarized in Acta Cryst. (1995), A51, 592±595. Turning to changes of the crystallographic information supplied by ITA5 as compared to the previous edition, it should ®rst be mentioned that the incorporation of the double-glide-plane symbol `e' into spacegroup symbols has been completed throughout the volume. This means that, in addition to glide planes a, b, c, d, n used before 1995, a sixth symmetry element appears in all parts (in centred cells only). Secondly, subgroup and supergroup data have been changed by adding space-group numbers and rearranging the group symbols according to rising index and falling spacegroup number. This applies particularly to Part 7 as the main part of ITA and facilitates dealing with the various symbols. It is recommended for future editions to obey these rules in the examples of subgroups given in Chapter 4.3 (by E. F. Bertaut), too. Thirdly, there are several improvements that apply to individual groups only, such as changes in the sequence of the positions and symmetry operations for the `rhombohedral axes' descriptions of certain R groups. While changes of Parts 1, 3±6, 11±13 (by Th. Hahn, A. Looijenga-Vos, M. J. Buerger, E. F. Bertaut, H. Arnold, W. Fischer, E. Koch, H. Burzlaff, H. Zimmermann, Y. Billiet) are mainly of formal character, substantial revisions and reorganizations of the text have been carried out in the remaining parts. They can in most cases be considered successful in expressing the fundamentals more clearly, apparently stimulated by the feedback from students, and in taking new developments into account. Examples are the presentation of general and special re ̄ection conditions (Section 2.2.13) and the way monoclinic space groups book reviews