Chapter 6 develops in detail the theory of hyperreal numbers; i.e., the field of real numbers together with infinitesimals and their algebraic transformations. It applies, in this special case, the principles of extension and transfer from the ordinary field of real numbers to that of the hyperreals. The chapter provides a detailed analysis of the algebraic structure of the set of limited (or bounded) numbers and outlines the rules of operation for hyperreal numbers in general. It concludes with a study of hypernatural, hyperinteger, and hyperrational numbers, which are important in the formulation of nonstandard economic theory.