  In this article, the ring of polynomials is studied in a systematic way
through the theory of monoid rings. As a consequence, this study provides
natural and canonical approaches in order to find easy and rigorous proofs and
methods for many facts on polynomials and formal power series; some of them as
sample are treated in this note. Besides the universal properties of the monoid
rings and polynomial rings, a universal property for the formal power series
rings is also established.
