"This set of notes is an activity-oriented introduction to linear and multilinear algebra. The great majority of the elementary results in these subjects are straightforward and can be verified by the thoughtful student. Indeed, the main point of these notes is to convince the beginner that the subject is accessible. In the material that follows, numerous indicators suggest activity on the part of the reader: words such as "proposition", "example", "theorem", "exercise", and "corollary", if not followed by a proof (and proofs here are scarce) or a reference to evidence, are invitations to verify the assertions made. These notes are intended to accompany an (academic) year-long course at the advanced undergraduate or beginning graduate level. (With judicious pruning, most material can be covered in a two-term sequence.) The text is also suitable for a lecture-style class, with the instructor proving some results while leaving others as exercises for the students. This book has tried keeping the facts about vector spaces and inner product spaces separate. Many beginning linear algebra texts conflate the material on these two vastly different subjects