Sheffer polynomials, monomiality principle, algebraic methods and the theory of classical polynomials

The Sheffer polynomials and the monomiality principle, along with the underlying operational formalism, offer a powerful tool for investigation of the properties of a wide class of polynomials. We present, within such a context, a self-contained theory of such familiar systems of polynomials as the Euler, Bernoulli, Bessel and other clasical polynomials and show how the derivation of some of their old and new properties is greatly simplified.