Introduction
1. Poincaré and his disk
2. Differential equations with algebraic coefficients over arithmetic manifolds
3. Poincaré and analytic number theory
4. The theory of limit cycles
5. Singular points of differential equations: On a theorem of Poincaré
6. Periodic orbits of the three body problem: Early history, contributions of Hill and Poincaré, and some recent developments
7. On the existence of closed geodesics
8. Poincaré’s memoir for the Prize of King Oscar II: Celestial harmony entangled in homoclinic intersections
9. Variations on Poincaré’s recurrence theorem
10. Low-dimensional chaos and asymptotic time behavior in the mechanics of fluids
11. The concept of “residue" after Poincaré: Cutting across all of mathematics
12. The proof of the Poincaré conjecture, according to Perelman
13. Henri Poincaré and the partial differential equations of mathematical physics
14. Poincaré’s calculus of probabilities
15. Poincaré and geometric probability
16. Poincaré and Lie’s third theorem
17. The Poincaré group
18. Henri Poincaré as an applied mathematician
19. Henri Poincaré and his thoughts on the philosophy of science

Henri Poincaré (1854–1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions. He revolutionized celestial mechanics, discovering deterministic chaos. In physics, he is one of the fathers of special relativity, and his work in the philosophy of sciences is illuminating. --- summary provided by publisher