An Elementary Introduction to Direct Methods; H. Schenk. Structure Factor Algebra: Structure Invariants and Seminvariants; G. M. Sheldrick. Structure Invariants and Origin Definition; H. Krabbendam. The Sayre Equation; M. W. Woolfson. The Cochran Distribution; M. W. Woolfson. Determinational Inequalities Lead to Triplet and Quartet Relationships; H. A. Hauptman. The Calculation of Normalized Structure Factors and of Triplet Invariants; D. Viterbo. Starting Set Determination; P. T. Beurskens. Symbolic Addition; H. Schenk. Tangent Formula, Tangent Refinement and Multisolution Methods; M. W. Woolfson. Quartets and Other Phase Relationships; H. Schenk. The Joint Probability Distribution of Three Structure Factors Leading to a Distribution for the Triplet Phase Sum; R. Peschar. Some Applications of Probability Theory in Direct Methods; S. Fortier, et al. The Neighborhood Principle and the Extension Concept; H. A. Hauptman. The Method of Representations of Structure Seminvariants: The General Background; C. Giacovazzo. Introduction to Maximum Entropy; G. Bricogne. Direct Methods Packages in 1990; C. J. Gilmore. Patterson Methods; P. Tollin. Optimal Symbolic Phase Determination; R. Peschar, et al. Random Approaches to the Phase Problem; M. W. Woolfson. 27 additional articles. Index.