The class group of a number field is an invariant that underscores some of its algebraic/arithmetic complexity much like the Picard group of a variety emphasizes the intricacy of algebraic/geometric structures on it. For Galois extensions of the rationals, these class groups do correlate to Galois groups when they are considered along some very special towers studied by Iwasawa. The $\Lambda$-fication principal originates here and involves endowing this structure on the inverse limit $X$ by the action of the Iwasawa algebra $\Lambda$. We will describe this construction in the context of class groups and L functions. This talk serves as an introduction to the Main Conjecture of Iwasawa theory and there are no number theoretic prerequisites.