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This book emphasizes the use of polynomials, and more generally, rational functions, as the vehicle for the development of linear algebra and linear system theory. This is a powerful and elegant idea, and the development of linear theory is leaning more toward the conceptual than toward the technical. However, this approach has its own weakness. The stumbling block is that before learning linear algebra, one has to know the basics of algebra. Thus groups, rings, fields, and modules have to be introduced. This we proceed to do, accompanied by some examples that are relevant to the content of the rest of the book.