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The present volume treats the symmetries of one-, two-, and three-dimensional space groups and point groups in direct space. It thus corresponds to Vol. 1 of IT (1935) and to Vol. I of IT (1952). Not included in Volume A are `partially periodic groups', like layer, rod and ribbon groups, or groups in dimensions higher than three. The treatment is restricted to `classical' crystallographic groups (groups of rigid motions); all extensions to `generalized symmetry', like antisymmetric groups, colour groups, symmetries of defect crystals, etc., are beyond the scope of this volume.
Compared to its predecessors, the present volume has been considerably increased in size. There are three reasons for this: (i) Extensive additions and revisions of the data and diagrams in the Space-group tables (Section 6 and 7), which lead to a standard lay-out of two pages per space group (see Section 2.2), as compared to one page in IT (1935) and IT (1952); (ii) Replacement of the introductory text by a series of theoretical sections; (iii) Extension of the synoptic tables.