This textbook, designed for at least one and one-half year's work in algebra, is intended for the use of those schools which find a one-book course best adapted to their needs. Experience thoroughly justifies a careful review at the beginning of the third half year's work. As the first twenty-three chapters contain the greater portion of the usual first year's work in algebra, it seemed best to follow them with the review material. Each topic is given a broader and more advanced treatment than is permissible in first-year work. New matter is used throughout, and many new applications are given in order to make a fresh and inviting appeal to the student. In the remaining chapters the aim has been to include those topics considered necessary by the best secondary schools, and to treat each in a clear, practical, and attractive manner. The exercises and problems have been tested by class use. While their number is ample it is not excessive. [For "Complete School Algebra. Teachers' Edition," see ED622734.]