Daniel François Coray (1947-2015) was Professor of Mathematics at the University of Geneva. His research interests spanned algebraic number theory, arithmetic of algebraic varieties, enumerative geometry, theoretical applications of computer methods and mathematical modeling of spatial concepts. His achievements in research were matched by his passion for teaching throughout his career. Daniel Coray passed away unexpectedly in June 2015 in Geneva only two months after he had completed the French version of this book manuscript.

Chapter 1. Diophantus of Alexandria.- Chapter 2. Algebraic closure; affine space.- Chapter 3. Rational points; finite fields.- Chapter 4. Projective varieties; conics and quadrics.- Chapter 5. The Nullstellensatz.- Chapter 6. Euclidean rings.- Chapter 7. Cubic surfaces.- Chapter 8. p-adic completions.- Chapter 9. The Hasse principle.- Chapter 10. Diophantine dimension of fields.