The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter contains: an introduction and summary; three to six sections, each devoted to one use class and containing a general introduction, questions, and comments; suggestions for teaching or illustrating a given concept; questions which test understanding of the ideas presented; and notes and commentary, with reasons for selecting particular use classes, related research, and short essays on issues related to applying the concepts. Topics of the chapters include: (1) use of single numbers (counts, measures, locations, ratio comparisons, codes, and derived formula constraints); (2) use of ordered pairs, triples, or n-tuples (counts, measures, locations, ratios, codes, and combined uses); (3) uses of collections of numbers (domains, data sets, neighborhoods, and solution sets); and (4) uses of variables (formulas, unknowns, properties, and storage locations). (JN)