"While the earlier edition of the Gilbert book was suitable for second and third year mathematics students, the level of writing was challenging for first year students. I was very pleased to find that the Gilberts have added a good number of meaningful examples and exercises at the appropriate level for such students. Moreover, in carefully doing so, they have not destroyed their crisp and efficient style of writing.""I am...quite enthusiastic about the arrangement of topics which the Gilberts have chosen....The Gilberts Chapter 1 plays as a sort of overture, in which the main elements of vector space theory are laid out in a comfortable space, while due attention is paid to the role of computation. I think this type of start to a course would orient the students properly toward general vector space theory, rather than having them come upon the annoying complication of vector spaces after three or more weeks spent exclusively in computation and row reduction."