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 functionl-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, the real number system is introduced, the coordinate plane developed, and the ring of real valued functions over the real numbers defined. Solutions of polynomial equations and inequalities are discussed in graphical terms. Other functions discussed include exponentials, absolute value, and greatest integer. (SD)