| Foundations of Number Theory: The greatest common divisor of two numbers / Part 1： |
| Prime numbers and factorization into prime factors |
| The greatest common divisor of several numbers Number-theoretic functions Congruences |
| Quadratic residues Pell's equation |
| Brun's Theorem and Dirichlet's Theorem: Introduction / Part 2： |
| Some elementary inequalities of prime number theory Brun's theorem on prime pairs Dirichlet's theorem on the prime numbers in an arithmetic progression |
| Further theorems on congruences |
| Characters; $L$-series; Dirichlet's proof |
| Decomposition into Two, Three, and Four Squares: Introduction Farey fractions / Part 3： |
| Decomposition into two squares Decomposition into four squares |
| Introduction |
| Lagrange's theorem |
| Determination of the number of solutions Decomposition into three squares |
| Equivalence of quadratic forms |
| A necessary condition for decomposability into three squares |
| The necessary condition is sufficient |
| The Class Number of Binary Quadratic Forms: Introduction Factorable and unfactorable forms Classes of forms / Part 4： |
| The finiteness of the class number Primary representations by forms |
| The representation of $h(d)$ in terms of $K(d)$ Gaussian sums |
| Appendix |
| Kronecker's proof |
| Schur's proof |
| Mertens' proof Reduction to fundamental discriminants |
| The determination of $K(d)$ for fundamental discriminants |
| Final formulas for the class number Appendix |
| Exercises: Exercises for part one Exercises for part two Exercises for part three |
| Index of conventions |
| Index of definitions |
| Index |
| Foundations of Number Theory: The greatest common divisor of two numbers / Part 1： |
| Prime numbers and factorization into prime factors |
| The greatest common divisor of several numbers Number-theoretic functions Congruences |
| Quadratic residues Pell's equation |
| Brun's Theorem and Dirichlet's Theorem: Introduction / Part 2： |
| Some elementary inequalities of prime number theory Brun's theorem on prime pairs Dirichlet's theorem on the prime numbers in an arithmetic progression |
