From the PREFACE. In the present Introduction to Determinants we have included, in addition to what appears in the authors' Theory of Equations, an Appendix in which the subject is illustrated by examples from Trigonometry and Coordinate Geometry. With this exception the present work is identical with the first Chapter of the second Volume of our Theory of Equations. The second Volume in its complete form will not be ready for publication for some time; we have therefore thought it desirable to bring out this Chapter in a separate form, simultaneously with the first Volume. This arrangement will probably be found convenient by students who do not aim at a more advanced study of the subject, as well as by others who may desire to obtain a knowledge of Determinants without any preliminary study of the Theory of Equations.