The primary goal of this book is to assist the student to develop the skills necessary to effectively employ the ideas of mathematics to solve military problems. At the simplest level I seek to promote an understanding of why mathematics is useful as a language for characterizing the interaction and relationships among quantifiable concepts, or in mathematical terms, variables. The text explores models of terrorism, attrition, search, detection, missile defense, radar, and operational reliability Throughout the text I emphasize the notion of added value and why it is the driving force behind military mathematical modeling. For a given mathematical model to be deemed a success something must be learned that was not obvious without the modeling procedure. Very often added value comes in the form of a prediction. In the absence of added value the modeling procedure becomes an exercise not unrelated to digging a ditch simply to fill it back up again.