The author of this text ranks among America's most influential teachers, and his stimulating lectures helped train many leaders in mathematical research. Maxime Bocher’s Introduction to Higher Algebra remains a favorite with students and teachers for a number of important reasons: comparatively, brief, it covers a vast amount of material; its elegant presentation of concepts and theorems is unsurpassed in the literature; its specific and concrete approach makes the content easier to learn and understand; and it offers a rich repository of often-neglected theorems. This text presents the fundamentals of higher algebra — including polynomials, determinants, matrices, and elimination theory — and a thorough foundation in algebraic principles. Beginning with an account of polynomials and their basic properties, it examines the properties of determinants and Laplace's development, multiplication theorem, bordered and adjoint determinants, the theory of linear dependence, linear equations, and related topics. A treatment of theorems concerning the rank of a matrix is followed by chapters on linear transformations and the combination of matrices, invariant, and bilinear forms. Additional topics include quadratic forms, factors of polynomials, general theorems on integral rational invariants, symmetric polynomials, polynomials symmetric in pairs of variables, and elementary divisors.