Guided mostly by the first ten pages of the second half of Serre's "A Course in Arithmetic", I'll talk about the Dirichlet L-functions, of which the Riemann zeta-function is a special case. I'll use their special properties to give a proof of Dirichlet's Theorem, which gives that the density of primes in arithmetic progressions and also, using the Legendre character, the density of primes that make the non-square integer a square modulo themselves. The talk should be accessible to all.