Many books have been written in a popular style to emphasize the importance of x-ray crystallography and to create interest in the wonderful findings of the workers in the field. A few books have been written with rigor for the benefit of the most advanced scholars. In between the extremes of popular and rigorous there is a gap. As a consequence of this gap, a very large proportion of the x-ray crystal-lographers actively engaged in the field in America today are working out structures successfully only because they have bridged the gap by having read a necessarily large number of those papers in the scientific journals which serve as signposts for the theory and the proper procedure. It is the purpose of the present text to furnish a common source in which the student may find condensed the teachings of the pioneers in crystallography. Although the lone investigator is borne in mind throughout the book, it has been hoped that the book may also be of use as a university text in a two-quarter course in structure analysis. Much of this book has been used as lecture material over a six-year period at the University of Utah (1947-1953) and, in the form of mimeographed lecture notes, has been under constant revision from the beginning. The first four chapters pertain to crystallography preparatory to the last five chapters on structure.