This book consists of the expanded notes from an upper level linear algebra course given some years ago by the author. Each section, or lecture, covers about a week's worth of material and includes a full set of exercises of interest. It should feel like a very readable series of lectures. The notes cover all the basics of linear algebra but from a mature point of view. The author starts by briefly discussing fields and uses those axioms to define and explain vector spaces. Then he carefully explores the relationship between linear transformations and matrices. Determinants are introduced as volume functions and as a way to determine whether vectors are linearly independent. Also included is a full chapter on bilinear forms and a brief chapter on infinite dimensional spaces.The book is very well written, with numerous examples and exercises. It includes proofs and techniques that the author has developed over the years to make the material easier to understand and to compute.

Donald S Passman, Richard Brauer Professor of Mathematics (Emeritus) at University of Wisconsin-Madison. PhD Harvard University 1964. Research interests include ring theory, group theory, group rings and enveloping algebras of Lie algebras. Author of six books and 185 published mathematics papers.Honors include: Member of the inaugural class of Fellows of the American Mathematical Society 2012, Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching, MAA 2000, Award for Distinguished University Teaching, MAA Wisconsin 1999, Underkofler Excellence in Teaching Award 1998, Plenary speaker, Canadian Math Soc. summer meeting, Windsor Ontario 1989, Member, Council of AMS 1984–1988, Main lecturer, CBMS Conference, Mankato State University 1985, Invited speaker, American Math Society meeting, Washington DC 1979, Invited speaker, 29th British Mathematical Colloquium, University of Edinburgh 1977, Lester R Ford Award for 'What is a group ring' 1976, Romnes Faculty Fellowship 1975–1980.Editor of various journals including: Journal of Algebra and its Applications, Proceedings of the AMS, Communications in Algebra, Algebras and Representation Theory, Beitrage zur Algebra und Geometrie, International J. of Mathematics, Game Theory and Algebra, vProceedings Edinburgh Math. Soc., Proceedings Royal Society of Edinburgh, Sao Paulo J. of Mathematical Sciences, Journal of Egyptian Math. Soc., Journal of Indian Math. Soc.