In preparing the present work, the author has endeavored to meet the needs of Colleges and Scientific Schools of the highest rank. The development of the subject follows in the main the author's College Algebra; but numerous improvements have been introduced. Contents:1. Definitions. Notation. Positive Integers, 2. Rational Numbers, 3. Addition and Subtraction of Algebraic Expressions, 4. Multiplication of Algebraic Expressions, 5. Division of Algebraic Expressions, 6. Integral Linear Equations, 7. Special Methods in Multiplication and Division, 8. Factoring, 9. Highest Common Factor. Lowest Common Multipile, 10. Fractions ......