This textbook combines the material of the "New First Course in Algebra" and the "New Second Course in Algebra" in a form convenient for use in courses of more than a year in length. A large amount of review material is to be found at the point where the second year of work commences, since it was felt that there should be an adequate opportunity for the pupil to return to the fundamentals of algebraic technique before proceeding with the more advanced work of the second year. As in the case of the former edition, emphasis has been placed on the Oral Exercises which appear at the beginning of the treatment of each new topic. The hint has also been used freely in the lists of written exercises in order to call the attention of the pupil to the best approach to the particular problem represented in the new exercises, before they have had a chance to develop wrong habits in the performance of their task. The work on graphs has been considerably modified in treatment to conform to modern tendencies in graphical presentation. The first approach to the subject is from the direction of graphing statistics. The pupil will probably already be familiar with graphs as they appear in the daily newspapers and current periodicals. This work is included early in the text as it is of interest to the student and tends to make them feel more at home in the subject of algebra. Throughout the book every effort has been made to provide the pupil with problems of real interest dealing with situations already more or less familiar.