Includes bibliographical references and index.

Introduction: Applications of pseudo-holomorphic curves to symplectic topology, J. Lafontaine and M. Audin: Examples of problems and results in symplectic topology; Pseudo-holomorphic curves in almost complex manifolds; Proofs of the symplectic rigidity results; What is in the book. . . and what is not...; Bibliography. Part 1: Basic symplectic geometry - An introduction to symplectic geometry, A. Banyaga: Linear symplectic geometry; Symplectic manifolds and vector bundles, Appendix: the Maslov class, M. Audin, A. Banyaga, F. Lalonde and L. Polterovich, Bibliography; Symplectic and almost complex manifolds, M. Audin: Almost complex structures, Hirzebruch surfaces, Coadjoint orbits (of U(n)), Symplectic reduction, Surgery?, Appendix: The canonical almost complex structure on the manifold of 1-jets of pseudo-holomorphic mappings between two almost complex manifolds, P. Gauduchon, Bibliography. Part 2: Riemannian geometry and linear connections - Some relevant Riemannian geometry J. Lafontaine: Riemannian manifolds as metric spaces, The geodesic flow and its linearisation, Minimal manifolds, Two-dimensional Riemannian Manifolds, An application to pseudo-holomorphic curves, Appendix: the isoperimetric inequality, M.-P. Muller, Bibliography; Connections lineaires, classes de Chern, theoreme de Riemann-Roch, P. Gauduchon: Connexions lineaires, Classes de Chern, Le theoreme de Riemann-Roch, Bibliographie. Part 3: Pseudo-holomorphic curves and applications - Some properties of holomorphic curves in almost complex manifolds, J, - C. Sikorav: The equation af = g in C, Regularity of holomorphic curves, Other local properties, Properties of the area of holomorphic curves, Gromov's compactness theorem for holomorphic curves, Appendix: Stokes' theorem for forms with differentiable coefficients, Bibliography; Singularities and positivity of intersections of J-holomorphic curves, D. McDuff: Elementary properties, Positivity of intersections, Local deformations, Perturbing away sing.

This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.