It is eleven years since the First Edition of Geometry of Crystallographic Groups appeared. This Second Edition expands on the first, providing details of a new result of automorphism of crystallographic groups, and on Hantzsche-Wendt groups/manifolds.

Crystalographic groups are groups which act via isometries on some n-dimensional Euclidean space, so-named because in three dimensions they occur as the symmetry groups of a crystal. There are short introductions to the theme before every chapter, and a list of conjectures and open projects at the end of the book.

Geometry of Crystallographic Groups is suitable as a textbook for students, containing basic theory of crystallographic groups. It is also suitable for researchers in the field, discussing in its second half more advanced and recent topics.

Contents:

• Definitions
• Bieberbach Theorems
• Classification Methods
• Flat Manifolds with b₁ = 0
• Outer Automorphism Groups
• Spin Structures and Dirac Operator
• Flat Manifolds with Complex Structures
• Crystallographic Groups as Isometries of ℍⁿ
• Hantzsche-Wendt Groups
• Combinatorial Hantzsche-Wendt Groups
• Open Problems

Readership: Researchers in geometry and topology, algebra and theory students, Institutes of Crystallography, University Chemistry departments.

Review of the First Edition:'This very precise and well written text is an extended version of the notes of the lectures given by the author at Gdańsk University for graduate students.' - The European Mathematical Society

Key Features:

• This is a mathematical book, but crystallography is also a popular topic within Chemistry and Physics. It is therefore a useful book for students of all three of these
• This book builds on the work of L S Charlap, Bieberbach Groups and Flat Manifolds, with many fresh and important insights and results
• New materials from the last two decades are detailed clearly