In recent years the x-ray fluorescence technique has become increasingly important in modern analysis and production control; it can be classified as a spectroscopical method for the determination of the elemental com position. Many articles treat this method; however, there exists no modern textbook suitable for the beginner as well as the practician and theoretician. In this monograph the author intends to fill this need to present the prin ciples of x-ray fluorescence analysis and to develop a theoretical under standing of the technique. Both principles and theory w.ill be treated exten sively, for they are the basis for successful practical application of the method. X-ray fluorescence, on the other hand, is often carried out exclusively because of its practical usefulness. For this reason theoretical investigations are used exclusively as a basis for practical work and the multitude of applications, which constitute the value of the x-ray fluores cence method, will be explained on the basis of simple theory. The idea to write this monograph originated and developed when efforts to train coworkers required a more complete treatise. I would like to thank the elBA Aktiengesellschaft in Basel, where this work originated, for generous support and permission to publish the book. The head of the Physics Department, Dr. E. Ganz, and my colleagues have contributed to this book by providing a stimulating working atmosphere. I am grateful to my associates, in particular Messrs. E. Eng, S. Gasser, and H. R.