This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. Beginning with a discussion of the rudiments of set theory, the authors lead readers through a construction of the natural number system and end with a discussion of the real numbers. Afterwards, students should be prepared for introductory courses in abstract algebra and real variables. AUTHORS: Norman Hamilton and Joseph Landin were both on the faculty at The University of Illinois. Dover also publishes Prof. Landin's Introduction to Algebraic Structures.