In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of particular importance. Part I of this book presents the necessary mathematical foundations and tools: the fundamentals of crystallography with special emphasis on symmetry, the theory of the crystallographic groups, and the formalisms of the needed crystallographic computations. Part II gives an insight into applications to problems in crystal chemistry. With the aid of numerous examples, it is shown how crystallographic group theory can be used to make evident the relationships between crystal structures, to set up a systematic order in the huge amount of known crystal structures, to predict crystal structures, to analyse phase transitions and topotactic chemical reactions in the solid state, to understand the formation of domains and twins in crystals, and to avoid errors in crystal structure determinations. Part III delves further into some specific topics, namely the isomorphic subgroups of space groups, the theory of phase transitions, and computer programs dedicated to crystallographic group theory. In this new edition, several topics have been extended to cover the latest scientific findings, a new chapter has been added dealing with pertinent computer programs, and references have been updated.

Review from previous edition Here we have a rigorous, carefully checked and polished text which, with its numerous examples and exercises, also perfectly fits the purpose of self-study ... This is a book that every crystallographer taking seriously their job should have on their shelf. * Acta Crystallographica B *
Structural crystallographers in biology, chemistry and physics meet symmetry and sometimes relatively complicated cases. More can be made of symmetry relations too. This book takes the reader beyond structure. The book shows how to make use of the symmetry relations described in International Tables as well as understand, for example, crystal structure types, analyse phase transitions, domain formation and twinning in crystals as well as to avoid errors in crystal structure determinations such as choice of incorrect space group. Numerous chapter exercises are a distinctive feature and offer the possibility to apply the material that has been learnt; solutions to the exercises are at the end of the book. * John R. Helliwell, School of Chemistry, The University of Manchester *

Ulrich Müller studied chemistry at Technische Hochschule in Stuttgart, Germany from 1959 to 1966 and gained a PhD in Inorganic Chemistry. He worked as a Scientific assistant at Universität Karlsruhe, Germany, with H. Bärnighausen from 1967 to 1970 and was a Professor of Inorganic Chemistry at Universität Marburg, Germany, from 1972 to 1992 and 2000 to 2005. He was a Professor of Inorganic Chemistry at Universität Kassel, Germany, from 1992 to 2000, and a visiting Professor at Universidad de Costa Rica, 1975 to 1977. He retired in 2005. Gemma de la Flor studied physics at the University of the Basque Country, Spain from 2004 to 2009 and gained a PhD in Physics at the University of the Basque Country in 2014. She was a post-doc and a lecturer at the University of the Basque Country from 2014 to 2016. She held a post-doc position at Universität Hamburg, Germany, with Professor Boriana Mihailova from 2016 to 2018. Since 2019 she has been a research associate in the petrophysics department at the Karlsruher Institut für Technologie, Germany.