It is nonnal for the preface to explain the motivation behind the writing of the book. Since many good books dealing with the general theory of crystal defects already exist, a new book has to be especially justified, and here its main justification lies in its treatment of crystal- line interfaces. About 1961, the work of the author, essentially based on the fundamental work of Professor F. C. Frank, started to branch away from the main flow of thought in this field and eventually led to a general geometrical theory which is presented as a whole for the first time in this book. Although nearly all that is presented has already been published in different journals and symposia, it might be difficult for the reader to follow that literature, as a new terminology and new methods of analysis had to be developed. Special emphasis is given to discussion and many diagrams are included in order that a clear view of the basic concepts be obtained. Intennediate summaries try to bring out the main points of the chapters. Instead of specific exercises, general suggestions for them are given. The part up to chapter 9 is considered more or less as introductory, so that the book can be studied without specific knowledge of crystals and crystal defects. The presentation of that part developed out of lectures given by the author at the Swiss Federal Institute of Technology (ETH) in Zurich.