This textbook furnishes abundant material for an intelligent review of the mathematics given in a large number of high schools, and it is the hope of the authors that other teachers may find the book useful in the hands of their pupils. The first-year review is intended to cover the work ordinarily done in the first-year mathematics course of the average high school. Similarly, the second-year outline furnishes a thorough review of the work usually given in that year. The third-year review covers the ordinary course in intermediate algebra and, with what precedes, meets college-entrance requirements. The authors have placed at the end of the book an outline of a tentative minimum course for one and one-half years of mathematics in the effort to initiate a plan for the standardization of high-school mathematics.