Preface -- In the past few years there has been a great resurgence of interest in mathematics on both the secondary and undergraduate levels, and a growing recognition that the courses traditionally offered do not exhaust the mathematics which it is both possible and desirable to teach at those levels. Of course, not all modern mathematics is accessible; some of it is too abstract to be comprehensible without more training in mathematical thinking, and some of it requires more technical knowledge than the young student can have mastered. Happily, the theory of numbers presents neither of these difficulties. The subject matter is the very concrete set of whole numbers, the rules are those the student has been accustomed to since grade school, and no assumption need be made as to special prior knowledge. To be sure, the results are not directly applicable in the physical world, but it is difficult to name a branch of mathematics in which the student encounters greater variety in types of proofs, or in which he will find more simple problems to stimulate his interest, challenge his ability, and increase his mathematical strength. For these and a number of other reasons, both the School Mathematics Study Group and the Committee on Undergraduate Programs have advocated the teaching of number theory to high school and college students.