The growth of operations research during the past several years has been phenomenal. Throughout its evolution, military problems have continually nourished the subject matter and provided interesting sources of research for its further development. As a consequence, military research organizations such as the Office of Naval Research have historically furnished the major support for work on the basic foundations of mathematics and management science necessary to the continued growth of operations research. Beginning with one or two basic textbooks in the early 1950's, most of the tools and techniques of this field have been found in specialized textbooks and the open literature. Recently several new and comprehensive textbooks became available for the classroom training of operations researchers at all levels. This is not surprising, since separate departments of operations research have been formed at various colleges and universities and now provide an opportunity for major study in this field at both the undergraduate and graduate levels. By and large the textbooks now available are not particularly oriented toward military applications, and a need for such a book appears to exist. This book has been written with a view toward filling that need. Its main purpose is to provide orientation for the practitioner who is interested in problem areas that have direct bearing on military applications. It is not a basic textbook designed to train an operations researcher in a comprehensive fashion, although certainly some of the material is amenable to classroom use. On the other hand, it is not a collection of isolated research papers. Rather, as the title indicates, it is an illustration of the basic tools and techniques used in solving certain problems of a military nature and application. Several areas have been explored in some detail, although certainly not every conceivable application or area is covered. Also, some applications are presented in terms that are broader than a specific military use. The coordinating theme of the book is the exploitation of mathematical models in the investigation of problems. For this reason the book begins with an extensive discussion of the various aspects of a mathematical model and its role in operations research. A case is made for the place of abstraction in the study of models and is illustrated with the simpler aspects of a Boolean algebra. Following this a rather comprehensive survey of probability and statistics is provided, emphasizing those points that are particularly significant for studying models. The book then proceeds through a variety of models from very specialized problems through search theory, simulation, and finally, inventory and reliability models. It then closes with a broad discussion of systems analysis.