Zeta functions coming from geometry III

We plan to give an overview of one of the most beautiful and fruitful tool for local-global problems in arithmetic geometry : zeta functions.
Classical zeta functions : Riemann zeta function, Dirichlet L-functions, prime number theorem and arithmetic progression theorem; Dedekind zeta functions and Artin L-functions, Chebotarev theorem. Zeta functions from algebraic geometry : Weil zeta function (for a variety over a finite field); Hasse-Weil L-functions (for a variety over a number field); L-function associated to a Galois representation or a modular form. Analytic theory of zeta functionsc: Analytic continuation and functional equations; Analytic estimates; Generalized Riemann hypothesis. Special values of zeta functions: Class number formula; Birch and Swinnerton Dyer conjecture; Brauer-Siegel type theorems.
If time permits, we will mention other conjectures on special values : Deligne, Beilinson, etc.