Includes bibliographical references.

The life of S. V. Kovalevskaya ; Kovalevskaya's mathematical work ; The KZB connection: Parametrizations, flat sections and deformation ; Jacobians of singularized spectral curves and completely integrable systems ; The hypergeometric equation, Askey-Wilson type solitons and rational curves with singularities ; Quantum discrete soliton equations ; Dual algebras of differential operators ; A link between two fundamental contributions of Kowalevski ; Monodromy deformation approach to the scaling limit of the Painleve first equation ; Kowalevski top revisited ; Some algebro-geometric integrable systems versus classical ones ; Painleve sixth equation as isomonodromic deformations equation of an irregular system ; Euler characteristics of theta divisors of Jacobians for spectral curves ; Reduction theory, elliptic solitons and integrable systems ; Schwarzian derivatives and uniformization ; Elliptic solitons and Heun's equation ; Generalized Kowalevski top: New integrable cases on 3) and so(4) ; Sur le probleme de la rotation d'un corps solide autour d'un point fixe