ALGEBRAIC NUMBER THEORY provides concisely both the fundamental and profound theory, starting from the succinct ideal theory (Chapters 1-3), turning then to valuation theory and local completion field (Chapters 4-5) which is the base of modern approach. After specific discussions on class numbers, units, quadratic and cyclotomic fields, and analytical theory (Chapters 6-8), the important Class Field Theory (Chapter 9) is expounded, and algebraic function field (Chapter 10) is sketched. This book is based on the study and lectures of the author at several universities.

Foreword / Prerequisites / Fields and Rings / Noetherian Rings and Dedekind Domains / Prime Decompositions in Extensions / Valuation Theory and Completions / Local Fields and Applications / Global Fields: Class Numbers and Units / Quadratic Fields and Cyclotomic Fields / Analytical Theory and Characters / Idèle and Class Field Theory / Algebraic Function Fields / Forms / Bibiography / Index.

Preface / Preliminaries / List of Symbols / Fields and Rings / Noetherian Rings and Dedekind Domains / Prime Decompositions in Extensions / Valuation Theory and Completions / Local Fields and Applications / Global Fields: Class Numbers and Units / Quadratic Fields and Cyclotomic Fields / Analytical Theory and Characters / Idèle and Class Field Theory / Algebraic Function Fields / Bibliography / Index.