This text is designed for a course in linear algebra and some of its applications for beginning students of science and engineering. It is an outgrowth of the notes from which I have lectured in recent years to undergraduate students of science and graduate students of the Faculty of Engineering at the University of Manitoba. I have found that an average student of science or engineering finds the vast existing literature on the theory and applications of matrices rather formidable, and I hope that the present text will develop understanding and grasp of the basic concepts. It will also bridge the gap between elementary books and the more advanced volumes on the subject.