Crystallographic groups are groups which act in a nice way and via
isometries on some n-dimensional Euclidean space. They got their
name, because in three dimensions they occur as the symmetry groups
of a crystal (which we imagine to extend to infinity in all
directions). The book is divided into two parts. In the first part,
the basic theory of crystallographic groups is developed from the
very beginning, while in the second part, more advanced and more
recent topics are discussed. So the first part of the book should
be usable as a textbook, while the second part is more interesting
to researchers in the field. There are short introductions to the
theme before every chapter. At the end of this book is a list of
conjectures and open problems. Moreover there are three appendices.
The last one gives an example of the torsion free crystallographic
group with a trivial center and a trivial outer automorphism
group.This volume omits topics about generalization of
crystallographic groups to nilpotent or solvable world and
classical crystallography. We want to emphasize that most theorems
and facts presented in the second part are from the last two
decades. This is after the book of L Charlap "Bieberbach groups and
flat manifolds" was published.
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