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 bookโฆ 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 linรฉaires, classes de Chern, thรฉorรจme 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 Gromovโs Schwarz lemma as an estimate of the gradient for holomorphic curves -- VIII Compactness -- IX Exemples de courbes pseudo-holomorphes en gรฉomรฉtrie riemannienne -- X Symplectic rigidity: Lagrangian submanifolds -- Authorsโ addresses

1. Mathematics
2. Topological groups
3. Lie groups
4. Differential geometry
5. Mathematics
6. Differential Geometry
7. Topological Groups
8. Lie Groups