These are homework problems and my solutions for an introductory algebraic number theory class I took in Fall 2006. The text for the class was *Algebraic Number Theory* by J.S. Milne, available (for free) here.

**Caveat lector: **I make no claim to the correctness of the solutions here, use them at your own risk.

- Sums of squares, Euclidean domains, PIDs, primes vs irreducibles: Problems, Solutions
- Integral closure, rings of integers: Problems, Solutions
- Field extensions, discriminants, integral basis: Problems, Solutions
- Orders, Dedekind domains: Problems, Solutions
- Ideal classes, more Dedekind domains: Problems, Solutions
- Ramification: Problems, Solutions
- Class numbers, unramified/ramified extensions: Problems, Solutions
- Lattices, Minkowski's Theorem: Problems, Solutions
- Dirichlet's Units Theorem, quadratic fields, cubic fields: Problems, Solutions
- More on units: Problems, Solutions

*Last updated: 5 December, 2006*