Analytic Number Theory:

1.

Dirichlet series and Euler products

2.

Characters on abelian groups

3.

The Riemann zeta function

(a)

Poisson summation, analytic continuation, and the functional equation for the zeta function

(b)

Zeros of the zeta function, trivial, non-trivial, Riemann Hypothesis

4.

$L$-series, Prime Number Theorem, distribution of prime numbers

5.

Dirichlet's theorem on primes in arithmetic progressions

6.

Prime Number theorem for arithmetic progressions