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