This Article Illustrates How Polynomials and Polynomial Matrices Can Be Used to Describelinear Systems. The Focus Is Put on the Transformation to and from the State-Space Equations, Because It Is a Convenient Way to Introduce Gradually the Most Important Properties of Polynomials and Polynomial Matrices, Such As: Coprimeness, Greatest Common Divisors, Unimodularity, Column- and Row- Reducedness, Canonical Hermite or Popov Forms.