Beginning in the early 1930s, most crystal structures were solved from analysis of the Patterson function. In 1952, a series of derivations revealed that crystal structures could be solved from the direct manipulation of the phases of Bragg reflections. The new approaches, known as direct methods, became immediately popular due to their relatively low computational requirements and their capacity to solve equal atom structures. Since that time, direct methods have become, to a large extent, the methods of choice. There are, however, structures which resist solution by direct methods;Through the years some researchers have continued to explore the intricacies of Patterson analysis. This research has developed to the point where complete structure determinations can now be made automatically on very complex structures. Reported here is an "ab initio" Patterson-based method, which is unique in that it requires no prior knowledge about the structure. This method has been automated in the form of a computer program called ALCAMPS. This dissertation will deal primarily with the theory and development of Patterson analysis, embodied in ALCAMPS, and its application to the solution of complex real crystal structures;To illustrate the ALCAMPS procedure, a hypothetical two-dimensional structure determination will be discussed, followed by a more detailed discussion of ALCAMPS, including many of the statistical tests and calculations which contribute to the accuracy of the results. ALCAMPS has been successfully applied to the solution of sixteen structures to date. Detailed discussions of eight of these structure solutions will be included. Conclusions about ALCAMPS and about the resulting increased power of Patterson analysis will be made;Fourteen crystal structure determinations have been carried out during the course of this research. Of these, four will be discussed in detail;The computer program PIKR serves a very important purpose in our automatic solution of crystal structures using Patterson analysis and will be discussed. This program calculates the positions and;heights of all peaks in the Patterson or Patterson superposition maps which are used; *DOE Report IS-T-1097. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy.