I will start by presenting the basic notions of Set Theory such as ordinal and cardinal numbers and afterwards I will review some classical applications of Set Theory to Topological Groups, Banach Algebras and Homological Algebra. I will try to give an intuition of why Set Theory applies to those situations. Following this, I will present some more recent applications of Set Theory to C*-algebras and speculate on how ultimately a connection to mathematical physics may result.