During the past seven years I have been involved in the investigation of high power microwave sources for accelerator and radar applications. As for many others before me, the starting point of this book was a collection of notes on theoretical topics out of the material I had been working on. The notes were the core of a course for graduate students at Cornell University. When I started to prepare these notes it seemed a fairly straight-forward and not very time-consuming task since I had most of the material well organized. Today, three years after the preparation of the first notes, I can only wonder how naive this thought was. Most of my work was oriented towards analytic and quasi-analytic tech niques for the investigation of the interaction of an electron beam with elec tromagnetic waves. These topics are presented in Chaps. 4 and 6. However, for a systematic elaboration of these topics it was necessary to provide some general background, therefore parts of what are today Chaps. 2, 3, and 5 were prepared. Related topics of acceleration concepts were also prepared to some extent but I ran out of time and the material (Chap. 8) was not delivered. In the meantime, various sections of this book were taught at the Technion Israel Institute of Technology and Ben-Gurion University. In the last version I included a discussion on free electron lasers (Chap. 7).