New material in the second online edition of Volume A1

In Chapter 1.4, the mathematical background of the subgroup tables has been extended to the theory of the minimal supergroups of the space groups.

Chapter 1.6 is new for this edition and provides instructions on how to build trees of group-subgroup relations for crystal structures that can be derived from a high-symmetry structure type (aristotype). Trees of this kind are useful for showing crystallographic relations between crystal-structure types and between the polymorphic forms of a compound.

Also new for this edition is Chapter 1.7 on the Bilbao Crystallographic Server. It describes the databases and computer programs that are related to the subjects of the volume.

In Chapter 2.1, a detailed discussion of the listed supergroup data and a description of a procedure for the complete derivation of the minimal supergroups from the listed (complete) data on maximal subgroups have been added.

Chapters 1.1, 1.2, 1.5 and 3.1 have also been revised and all known errors in the first edition have been corrected.