IN this tract I have tried to present the main portions of the theory of integral equations in a readable and, at the same time, accurate form, following roughly the lines of historical development. I hope that it will be found to furnish the careful student with a firm foundation which will serve adequately as a point of departure for further work in this subject and its applications. At the same time it is believed that the legitimate demands of the more superficial reader, who seeks results rather than proofs, will be satisfied by the precise statement of these results as italicized, and therefore easily recognized, theorems. The index has been added to facilitate the use of the booklet as a work of reference. In these days of rapidly multiplying voluminous treatises, I hope that the brevity of this treatment may prove attractive in spite of the lack of exhaustiveness which such brevity necessarily entails if the treatment, so far as it goes, is to be adequate.