This is a comprehensive textbook on J-holomorphic curves and symplectic topology, authored by Dusa McDuff and Dietmar Salamon. The book is divided into 12 chapters and several appendices, covering a wide range of topics in symplectic geometry. It begins with an introduction to symplectic manifolds, moduli spaces, and Gromov-Witten invariants. The core of the book is devoted to the study of J-holomorphic curves, their properties, and the associated moduli spaces. It discusses the nonlinear Cauchy-Riemann equations, transversality, compactness, and the behavior of curves under various conditions. The text also explores stable maps, Gromov-Witten invariants, and their applications in symplectic topology. It includes detailed discussions on Hamiltonian perturbations, the gluing of J-holomorphic curves, and quantum cohomology. The book also covers Floer homology, spectral invariants, and the symplectic vortex equations. Appendices provide additional background on Fredholm theory, elliptic regularity, the Riemann-Roch theorem, stable curves, and singularities. The text is written for advanced students and researchers in mathematics, particularly those interested in symplectic geometry and related areas. It is a fundamental reference for understanding the theory of J-holomorphic curves and its applications in symplectic topology. The book includes a bibliography and a list of symbols, making it a valuable resource for both learning and research.This is a comprehensive textbook on J-holomorphic curves and symplectic topology, authored by Dusa McDuff and Dietmar Salamon. The book is divided into 12 chapters and several appendices, covering a wide range of topics in symplectic geometry. It begins with an introduction to symplectic manifolds, moduli spaces, and Gromov-Witten invariants. The core of the book is devoted to the study of J-holomorphic curves, their properties, and the associated moduli spaces. It discusses the nonlinear Cauchy-Riemann equations, transversality, compactness, and the behavior of curves under various conditions. The text also explores stable maps, Gromov-Witten invariants, and their applications in symplectic topology. It includes detailed discussions on Hamiltonian perturbations, the gluing of J-holomorphic curves, and quantum cohomology. The book also covers Floer homology, spectral invariants, and the symplectic vortex equations. Appendices provide additional background on Fredholm theory, elliptic regularity, the Riemann-Roch theorem, stable curves, and singularities. The text is written for advanced students and researchers in mathematics, particularly those interested in symplectic geometry and related areas. It is a fundamental reference for understanding the theory of J-holomorphic curves and its applications in symplectic topology. The book includes a bibliography and a list of symbols, making it a valuable resource for both learning and research.