The purpose of this little book is to give the reader a convenientintroduction to the theory of numbers, one of the most extensiveand most elegant disciplines in the whole body of mathematics. The treatment throughout is madeas brief as ispossible consistent with clearness and is confinedentirely to fundamental matters. This is done because it is believedthat in this way the book may best be made to serve its purposeas an introduction to the theory of numbers.Numerous problems are supplied throughout the text. The exercises marked with a star are moredifficult than the others; they will doubtlessly appeal to the beststudents. Finally, this book is made up from thematerial used by the author in lectures in Indiana University during thepast two years; and the selection of matter, especially of exercises,has been based on the experience gained in this way.