1. Gaussian integers and integrality
2. Ideals
3. Lattices & Minkowski's "geometry of numbers"
4. The Class Number
5. Dirichlet's unit theorem
6. Extensions of Dedekind domains
7. Hilbert's ramification theory
8. Cyclotomic fields
9. Localization
10. Orders
11. One-dimensional schemes
12. Function fields
13. p-adic numbers
14. Valuations & completions
15. Local fields