This is a course in linear algebra. Vector spaces are introduced and are shown to have linear bases and a well-defined dimension. The study of linear transformations leads to matrices and methods for solving systems of linear equations by Gauss-Jordan elimination. A short study of permutations leads to the definition of the determinant, which in turn is used to solve characteristic equations needed to obtain the eigenvalues and eigenvectors of square matrices. This ultimately leads to their Jordan canonical forms. The final section is devoted to dual spaces, inner products, and tensor products.