Written for mathematics students in their first year at university, this book is virtually self-contained and the exposition comes close to programmed learning in that it develops slowly but inexorably from a narrow base. The aim is to make the student feel thoroughly at home with the theory of rings, fields, and vector spaces, and especially with the techniques of matrix manipulation. Throughout the book the author has tried to keep the needs of the learner paramount. Motivation is supplied for the next step and new topics are introduced with care. There is a wide range of exercises integrated into the chapters and suggestions for further reading are given at the end.