The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is intended to provide students with a general background in the analytical methods of mathematics and practice in reasoning with mathematical objects; other texts (Books 1-12) prepared for use with book O explore particular areas in depth. In this chapter a wide variety of mappings is developed. These include mappings of finite sets defined explicitly for each point, projections of Cartesian products, permutations, and the recursively defined mapping of n onto n!, as well as translations and "stretchers and shrinkers." Composition of mappings is discussed. Many applications, including percent and addition of lengths, are included. (SD)