Linear Algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed.  Itis a core topic of study within fields as diverse as : business economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of the text lies in the large number of examples and the step-by-step explanation of each topic as it is introduced.  It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available on line at http://www.oup.co.uk/companion/singh. The miscellaneous exercises at the end of each chapter are comprised of questions from past exam papers from various universities, helping to reinforce the reader's confidence.  also included, general at the beginning of sections, are short historical biographies of the leading players in the field of linear algebra to provide context for the topics covered. The dynamic and engaging style of this book includes frequent question and answer section to test the reader's understanding of the methods introduced, rather than encouraging role of learning.  When first encountered, the subject can appear abstract and students will sometimes struggle to see its relevance; to counter this, the book also contains interviews with key people who use linear algebra in practice, professionally and academically.  It will be an invaluable resource for undergraduate students in mathematics, the physical science and engineering. Kuldeep Singh is Senior Lecturer in Mathematics at the University of Hertfordshire.