This book is designed so tbat it may be used in several ways: it can be used for self study, as a guide for tutonally directed work, or as a supplementary text or source of problems for an ordinary first or second course in number theoru. Tne aim of the book is similar to that of Aufgaben and Lenrsatze aus der Analysis by Polya and Szeyo. A considerable part of the work consists of sets of problems culminatiny m well known theorems. In this way muck of the material of an elementary course in number theory is covered« Moreover, many theorems not often met in suck elementary courses, but which require little or no greater sophistication, are included.