Textbook in PDF format

This book is based on lecture-courses given by the author at the University of Paris. Although designed to meet the needs of French undergraduates, it covers the beginning algebra course in an American University and the average Honors mathematics course in a British University. The book contains a thorough treatment of linear algebra and can therefore be used as an algebra textbook by the student throughout his undergraduate career.
The topics covered in this book are those which are universally considered to be essential for the future mathematician or physicist: sets and functions; groups, rings, fields, complex numbers; vector spaces, linear mappings, matrices; finite-dimensional vector spaces, systems of linear equations, determinants, Cramer's formulae; polynomials, rational fractions, algebraic equations; reduction of matrices. This choice of subject-matter reflects the evolution of mathematics in the last half-century, and we have thought it proper that this evolution should also be reflected by the use of a style which hitherto has been reserved for treatises addressed to professional mathematicians