Dirichlet's class number formula, Dirichlet style

The analytic class number formula relates the class number of a number field to the residue of a corresponding L-function. Dirichlet's original proof used the language of binary quadratic forms and a *beautiful* averaging argument. We'll define all of these things and look at Dirichlet's proof in the imaginary quadratic case, as well as, time permitting, some extensions (pun intended).