Translator's preface; 1. Landscapes; 2. A moment of rationality: Greece; 3. The constitution of classical algebra; 4. Figures, spaces, and geometries; 5. Limits: from the unconceived to the concept; 6. The concept of function and the development of analysis; 7. At the crossroads of algebra, analysis, and geometry: complex numbers; 8. New objects, new laws: the emergence of algebraic structures.