The Rietveld method is a powerful and relatively new method for extracting detailed crystal structural information from X-ray and neutron powder diffraction data. Since such structural details dictate much of the physical and chemical attributes of materials, knowledge of them is crucial to our understanding of those properties and our ability to manipulate them. Since most materials of technological interest are not available as single crystals but often are available only in polycrystalline or powder form, the Rietveld method has become very important and is now widely used in all branches of science that deal with materials at the atomic level. This book, a collaboration by many authorities in the field, is intended primarily to have tutorial and advisory value for those who already have some experience with this important method, but an introductory chapter enables the book to be used as a first text for researchers starting in this area of science. The audience is thus comprised of all scientists using the method: graduate students who may be starting research in this area, powder diffraction specialists, crystallographers, physicists, chemists, and materials scientists.