This detailed investigation of the real number system is geared toward students without great mathematical sophistication. The treatment presumes only a familiarity with the basic properties of natural numbers - though readers must be willing to apply themselves. Proceeding from a review of the natural numbers to the positive rational numbers, the text advances to the non-negative real numbers and the set of all real numbers. AUTHOR: Joseph Roberts received his Ph.D. in Mathematics at the University of Minnesota and taught for many years at Reed College in Portland, Oregon, where he is now Professor Emeritus of Mathematics.