The book of the famous Soviet mathematician A. G. Kurosh is a classic textbook on higher algebra. The simplicity and rigor of the presentation have long made the "Course" popular among students. The book covers most of the topics of the higher algebra course taught at the mathematical departments of universities: systems of linear equations, determinants and matrices, complex numbers, polynomials, linear and Euclidean spaces, quadratic forms, and the foundations of group theory. The publication is intended for students of mathematical and technical specialties of universities and all interested in algebra.