IN a considerable number of our colleges and universities the work of the first semester in mathematics is devoted to Algebra and Trigonometry. Usually Algebra is taken up first and then Trigonometry, or else the two subjects are studied on alternate days. Neither plan is quite satisfactory. It has therefore seemed to the writer that a single book, treating both subjects in a corre lated manner, might be of service both to student and teacher. In the present text the principal departures from the subject matter usually treated will be found in chapters 13 and 14. The chief aim has been to follow a/ mode and sequence of presentation which shall introduce the student who needs to apply his knowl edge of mathematics in his Other work as directly as possible to those facts and concepts which are most useful to him. For this reason much stress is laid on graphic methods in the chapters on linear and quadratic equations, and this is followed up later as opportunity arises. It is thought that the extra time so used will be more than made up when the student begins his study of Analytical Geometry, because he will have become grad ually familiar with the fundamental idea of this subject and need not readjust himself after an abrupt transition to a strange and mysterious realm.