1. The Factorization of Integers -- 2. Congruences -- 3. Quadratic Residues -- 4. Properties of Polynomials -- 5. The Distribution of Prime Numbers -- 6. Arithmetic Functions -- 7. Trigonometric Sums and Characters -- 8. On Several Arithmetic Problems Associated with the Elliptic Modular Function -- 9. The Prime Number Theorem -- 10. Continued Fractions and Approximation Methods -- 11. Indeterminate Equations -- 12. Binary Quadratic Forms -- 13. Unimodular Transformations -- 14. Integer Matrices and Their Applications -- 15. p-adic Numbers -- 16. Introduction to Algebraic Number Theory -- 17. Algebraic Numbers and Transcendental Numbers -- 18. Waringโ{128}{153}s Problem and the Problem of Prouhet and Tarry -- 19. Schnirelmann Density -- 20. The Geometry of Numbers