Introduction; 1. Diophantus; 2. Numbers and symbols; 3. Diophantine equations; 4. Evaluation of Diophantus' methods by historians of science; 5. Indeterminate quadratic equations; 6. Indeterminate cubic equations; 7. Diophantus and number theory; 8. Diophantus and the mathematicians of the 15th and 16th centuries; 9. Diophantus' methods in the works of Viete and Fermat; 10. Diophantine equations in the works of Euler and Jacobi: addition of points on an elliptic curve; 11. The geometric meaning of the operation of addition of points; 12. The arithmetic of algebraic curves; 13. Conclusion; 14. Supplement: the role of concrete numbers in Diophantus' 'Arithmetic'.
