This book helps students to master the material of a standard US undergraduate linear algebra course. The material is standard in that the topics covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard about the book is its audience: sophomores or juniors, usually with a background of at least one semester of Calculus. The help that it gives to students comes from taking a developmental approach - this book's presentation emphasizes motivation and naturalness, driven home by a wide variety of examples and by extensive and careful exercises.