The book begins with a detailed discussion of two problems that have played an extremely important role in the emergence of theoretical programming as an independent discipline. The principal goals in this book are to explain the line of thought that was followed in solving these problems, demonstrate the workings of the mathematical way of thinking, carefully analyze the different stages of descriptive analysis and problem formulation, and reveal the aesthetic component in the search for solutions - in other words, to try to turn the reader into a true witness of the process of discovering mathematical results. In the first part of the book the author considers the storage minimization packing, or storage problem schemas. The problem of storage packing is treated as an example that illustrates how to solve an application problem by means of mathematical methods. In the second part the author presents the theory of Yanov program schemas, a classical theory generally recognized as having served as a foundation of the mathematical theory of programming. This is analyzed as a methodological example that illustrates how a fully developed theory can be extended to a new class of phenomena and objects: program schemas and configurations of program schemas.