Any student studying linear algebra will welcome this textbook, which provides a thorough, yet concise, treatment of key topics in university linear algebra courses. The authors, who have extensive teaching experience, provide hundreds of examples and exercises with a complete list of solutions, to enable students to practise and master the standard methods. Crucially, the authors also give clear explanations of how the methods really work, so that readers can gain a sound understanding of the underlying theory. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book. At every stage the authors take care to ensure that the discussion is no more complicated or abstract than it needs to be and focuses only on the fundamental topics. Instructors can draw on the many examples and exercises to supplement their own assignments.