| Introduction / Chapter 1： |
| Integral Extensions / 1.1： |
| Localization / 1.2： |
| Norms, Traces and Discriminants / Chapter 2： |
| Norms and traces / 2.1： |
| The Basic Setup for Algebraic Number Theory / 2.2： |
| The Discriminant / 2.3： |
| Dedekind Domains / Chapter 3： |
| The Definition and Some Basic Properties / 3.1： |
| Fractional Ideals / 3.2： |
| Unique Factorization of Ideals / 3.3： |
| Some Arithmetic in Dedekind Domains / 3.4： |
| Factorization of Prime Ideals in Extensions / Chapter 4： |
| Lifting of Prime Ideals / 4.1： |
| Norms of ideals / 4.2： |
| A Practical Factorization Theorem / 4.3： |
| The Ideal Class Group / Chapter 5： |
| Lattices / 5.1： |
| A Volume Calculation / 5.2： |
| The Canonical Embedding / 5.3： |
| The Dirichlet Unit Theorem / Chapter 6： |
| Preliminary Results / 6.1： |
| Statement and Proof of Dirichlet's Unit Theorem / 6.2： |
| Units in Quadratic Fields / 6.3： |
| Cyclotomic Extensions / Chapter 7： |
| Some Preliminary Calculations / 7.1： |
| An Integral Basis of a Cyclotomic Field / 7.2： |
| Factorization of Prime Ideals in Galois Extensions / Chapter 8： |
| Decomposition and Inertia Groups / 8.1： |
| The Frobenius Automorphism / 8.2： |
| Applications / 8.3： |
| Local Fields / Chapter 9： |
| Absolute Values and Discrete Valuations / 9.1： |
| Absolute Values on the Rationals / 9.2： |
| Artin-Whaples Approximation Theorem / 9.3： |
| Completions / 9.4： |
| Hensel's Lemma / 9.5： |
| Appendices |
| Quadratic Reciproicty Via Gauss Sums / A： |
| Extension of Absolute Values / B： |
| The Different / C： |
| Solutions to Problems |
| Index |
| Introduction / Chapter 1： |
| Integral Extensions / 1.1： |
| Localization / 1.2： |
