Abstract: The study of commutative algebra is the study of commutative rings. So what are rings and what's so bloody interesting about them that they should capture the imaginations of so many mathematicians? In this talk I will introduce the notion of a ring and give many examples of rings, both commutative and non-commutative. We shall draw special attention to some of the rings of interest in the theory of factorization. Therefore we shall also find it convenient to compare and contrast the notions of prime and irreducible elements in rings.