Introduction: Applications of pseudo-holomorphic curves to symplectic topology.- 1 Examples of problems and results in symplectic topology.- 2 Pseudo-holomorphic curves in almost complex manifolds.- 3 Proofs of the symplectic rigidity results.- 4 What is in the book. and what is not.- 1: Basic symplectic geometry.- I An introduction to symplectic geometry.- II Symplectic and almost complex manifolds.- 2: Riemannian geometry and linear connections.- III Some relevant Riemannian geometry.- IV Connexions linéaires, classes de Chern, théorème de Riemann-Roch.- 3: Pseudo-holomorphic curves and applications.- V Some properties of holomorphic curves in almost complex manifolds.- VI Singularities and positivity of intersections of J-holomorphic curves.- VII Gromov's Schwarz lemma as an estimate of the gradient for holomorphic curves.- VIII Compactness.- IX Exemples de courbes pseudo-holomorphes en géométrie riemannienne.- X Symplectic rigidity: Lagrangian submanifolds.- Authors' addresses.
