This book is a comprehensive exposition of classical algebraic and analytic number theory, superseding the author's earlier work on algebraic numbers. It includes extensive material on class field theory and other topics. The book is intended for graduate students and researchers in mathematics. The text is written in a style that combines ideal and idele approaches without preference for either. It includes two proofs of the functional equation for the zeta function, illustrating different techniques. The book assumes knowledge of elementary algebra, including Galois theory, and some analysis for chapters on analytic number theory. It covers topics such as algebraic integers, completions, the different and discriminant, cyclotomic fields, parallelotopes, the ideal function, ideles and adeles, the zeta function and L-series, norm index computations, the Artin symbol, reciprocity law, class field theory, the existence theorem, local class field theory, L-series, the functional equation of the zeta function, Tate's thesis, density of primes, the Brauer-Siegel theorem, and explicit formulas. The book is divided into three parts: general basic theory, class field theory, and analytic theory. It is a key reference for understanding algebraic number theory and its applications.This book is a comprehensive exposition of classical algebraic and analytic number theory, superseding the author's earlier work on algebraic numbers. It includes extensive material on class field theory and other topics. The book is intended for graduate students and researchers in mathematics. The text is written in a style that combines ideal and idele approaches without preference for either. It includes two proofs of the functional equation for the zeta function, illustrating different techniques. The book assumes knowledge of elementary algebra, including Galois theory, and some analysis for chapters on analytic number theory. It covers topics such as algebraic integers, completions, the different and discriminant, cyclotomic fields, parallelotopes, the ideal function, ideles and adeles, the zeta function and L-series, norm index computations, the Artin symbol, reciprocity law, class field theory, the existence theorem, local class field theory, L-series, the functional equation of the zeta function, Tate's thesis, density of primes, the Brauer-Siegel theorem, and explicit formulas. The book is divided into three parts: general basic theory, class field theory, and analytic theory. It is a key reference for understanding algebraic number theory and its applications.