This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry finishing with a chapter on transformation groups; Part II is on quadratic forms and their geometry (Euclidean geometry) including a chapter on finite subgroups of 0 (2). Each of the 23 chapters concludes with a generous helping of exercises and a selection of these have solutions at the end of the book. The chapters also contain many examples both numerical worked examples (mostly in 2 and 3 dimensions) as well as examples which take some of the ideas further. Many of the chapters contain complements which develop more special topics and which can be omitted on a first reading. The structure of the book is designed to allow as much flexibility as possible in designing a course either by omitting whole chapters or by omitting the complements or specific examples. Language: English