The sixteen chapters of this book provide the core materials 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. Discussion of the set Z of integers is introduced by a series of games. After several problems involving negative numbers, the concept of additive inverse is discussed. Order properties of the integers and the solution of inequalities are presented. The systems (z,+) and (Z,-) are studied and their properties developed. Multiplication of integers is discussed by use of lines in a Cartesian coordinate system. (SD)