(CC BY) This textbook, published by Textbook Equity, is an open education resource released by The Saylor Foundation under a Creative Commons license. The original textbook, written by Kenneth Kuttler, was chosen by the Saylor Foundation, after a thorough peer review, to be the companion textbook to their online course. This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, this is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.