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Das Prinzip der Gruppentheorie ist gut einführt. Dennoch werden in diesem Lehrbuch zwei komplett neue Aspekte vorgestellt: besseres Verständnis durch die Konzentration auf Problemlösungsstrategien und der weitreichende Einsatz von Mathematica sowie die Einführung eines neuen Tools für die Photonik durch die Anwendung von Konzepten auf photonische Fasern und Kristalle.

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1 Preface
2 Introduction
I Basics of group theory
3 Symmetry operations and transformations of fields
4 Basic abstract group theory
5 Discrete symmetry groups for solid state physics and photonics
6 Representation theory
7 Symmetry in k-space
II Applications in electronic structure theory
8 Solution of the Schroedinger equation
9 Generalization to include the spin
10 Electronic energy bands
III Applications in photonics
11 Solution of Maxwell´s equations
12 Twodimensional photonic crystals
13 Threedimensional photonic crystals
14 Other Applications
A Mathematica Package Reference
B Connection of the group theory package to MPB and MEEP

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Wolfram Hergert, extraordinary professor in Computational Physics, is member of the Theoretical Physics group at University Halle-Wittenberg, Germany. Main subjects of his work are solid state theory, electronic and magnetic structure of nanostructures and photonics. Prof. Hergert has experience in teaching group theory and in applying Mathematica to physical problems. He has published in renowned journals, like Nature and Physical Review Letters, and edited a books on Computational Materials Science and Mie Theory. He is also coauthor of a book on Quantum Theory. R. Matthias Geilhufe is currently a post-doctoral researcher at the Nordic Institute for Theoretical Physics (Nordita) in Stockholm (Sweden). He completed his undergraduate and postgraduate studies at the Martin Luther University Halle-Wittenberg (Germany) with specialization in theoretical and computational physics and did his PhD in connection with the Max Planck Institute of Microstructure Physics in Halle. His main research interests are in condensed matter theory, in particular functional organic materials, Dirac materials, superconductivity, and topological band theory.

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