Group theory and its application to solid state physics which is well established. This book brings up two completely new aspects: its first aim is to provide a better understanding by focusing on problem solving, making extensive use of Mathematica tools; second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic fibers and crystals. The book is divided in three parts. Part I provides the basics of group theory. Already in the first part the authors go beyond the widely used standard examples but show already here the broad field of applications. The main focus in on problem solving by making use of the computer algebra system Mathematica which is used to visualize the concepts. Part II is devoted to applications in condensed matter physics and therefore to the electronic structure of materials. The extensive implementation of Mathematica and the concept of interactive work with book, computer algebra system, visualization tools and pen and paper leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory may also be applied to a totally different field, as follows in Part III. As photonic applications are discussed in parallel to the electronic case, the focus lies on photonic crystals in two and three dimension, and will partially be expanded to photonic-crystal fibres. The authors have developed Mathematica packages which can be downloaded from the book’s homepage. Analytic considerations, numerical calculations and visualization are done with the same software. Although the use of the Mathematica tools will be demonstrated on elementary examples, they can be applied to more complicated tasks of the reader’s own research.

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