Preface to the second edition Preface Chapter 1． Introduction 1．1． Symplectic manifolds 1．2． Moduli spaces： regularity and compactness 1．3． Evaluation maps and pseudocycles 1．4． The Gromov-Witten invariants 1．5． Applications and further developments Chapter 2． J-holomorpluc Curves 2．1． Almost complex structures 2．2． The nonlinear Cauchy-Riemann equations 2．3． Unique continuation 2．4． Criticalpoints 2．5． Somewhere injective curves 2．6． The adjunction inequality Chapter 3． Moduli Spaces and Transversality 3．1． Moduli spaces of simple curves 3．2． Transversality 3．3． A regularity criterion 3．4． Curves with pointwise constraints 3．5． Implicit function theorem Chapter 4． Compactness 4．1． Energy 4．2． The bubbling phenomenon 4．3． The mean value inequality 4．4． The isoperimetric inequality 4．5． Removal of singularities 4．6． Convergence modulo bubbling 4．7． Bubbles connect Chapter 5． Stable Maps 5．1． Stable maps 5．2． Gromov convergence 5．3． Gromov compactness 5．4． Uniqueness of the limit 5．5． Gromov compactness for stable maps 5．6． The Gromov topology Chapter 6． Moduli Spaces of Stable Maps 6．1． Simple stable maps 6．2． Transversality for simple stable maps 6．3． Transversality for evaluation maps 6．4． Semipositivity 6．5． Pseudocycles 6．6． Gromov-Witten pseudocycles 6．7． The pseudocycle of graphs Chapter 7． Gromov-Witten Invariants 7．1． Counting pseudoholomorphic spheres 7．2． Variations on the definition 7．3． Counting pseudoholomorphic graphs 7．4． Rational curves in projective spaces 7．5． Axioms for Gromov-Witten invariants Chapter 8． Hamiltonian Perturbations 8．1． Trivial bundles 8．2． Locally Hamiltonian fibrations 8．3． Pseudoholomorphic sections 8．4． Pseudoholomorphic spheres in the fiber 8．5． The pseudocycle of sections 8．6． Counting pseudoholomorphic sections Chapter 9． Applications in Symplectic Topology 9．1． Periodic orbits of Hamiltonian systems 9．2． Obstructions to Lagrangian embeddings 9．3． The nonsqueezing theorem 9．4． Symplectic 4-manifolds 9．5． The group of symplectomorphisms 9．6． Hofer geometry 9．7． Distinguishing symplectic structures Chapter 10， Gluing 10．1． The gluing theorem 10．2． Connected sums of J-holomorphic curves 10．3． Weighted norms 10．4． Cutoff functions 10．5． Construction of the gluing map 10．6． The derivative of the gluing map 10．7． Surjectivity of the gluing map 10．8． Proof of the splitting axiom 10．9． The gluing theorem revisited Chapter 11， Quantum Cohomology 11．1． The small quantum cohomology ring 11．2． The Gromov-Witten potential 11．3． Four examples …… Chapter 12． Floer Homology Appendix A． Fredholm Theory Appendix B． Elliptic Regularity Appendix C． The Riemann-Roch Theorem Appendix D． Stable Curves of Genus Zero Appendix E． Singularities and Intersections （written with Laurent Lazzarini） Bibliography List of Symbols Index
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