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. The set of rational numbers and its number line representation are developed from the set of integers in this chapter. Operations are defined in terms of mappings in the order: multiplication, division, addition, subtraction, and absolute value. The solution of equations with rational coefficients is introduced. (SD)