Global Theory:

1.

Dedekind domains

2.

Ring of integers in a number field

3.

Integral basis, fractional ideals, residue class field, norm of an ideal

4.

Ideal class group and class number

5.

Minkowski's theorem on convex regions

6.

Dirichlet's Unit theorem

7.

Decomposition of prime ideals in

(a)

arbitrary extensions of number fields

(b)

Galois extensions of number fields

(c)

Abelian extensions of number fields

8.

Ramification and inertial degrees, discriminant and different

9.

Decomposition and Inertia groups and fields

10.

Frobenius automorphism, Artin symbol

11.

Kronecker-Weber theorem

12.

Examples: Quadratic and Cyclotomic fields