When this course was first offered at Wisconsin two textbooks were required, one for linear algebra and another for differential equations. Neither was more than half covered and the discontinuities in terminology and notation caused much distress. An integrated treatment was clearly needed this book grew out of a response to that need It is not a long book. This book follows two converging lines of inquiry (vector spaces and matrices on the one hand, differential equations on the other) to their meeting in the context of linear systems of first order differential equations. The object is to introduce the unsuspecting sophomore to the beauties of both subjects in such a way as to persuade him of the usefulness of each without overwhelming him with the depth of either.