The book begins with the definition of time together with a brief description of its crucial properties and with the principles of the physical uniqueness and continuity of physical variables, which are essential for the natural tracking control synthesis. The book presents further new results on matrices, on polynomial matrices, on matrix polynomials and on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the proofs of the new observability, controllability, trackability and tracking conditions, as well as the natural tracking control synthesis for all five classes of the treated linear systems.