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Preface; 1 Integrability in classical mechanics; 2 Soliton equations and the Inverse Scattering Transform; 3 The hamiltonian formalism and the zero-curvature representation; 4 Lie symmetries and reductions; 5 The Lagrangian formalism and field theory; 6 Gauge field theory; 7 Integrability of ASDYM and twistor theory; 8 Symmetry reductions and the integrable chiral model; 9 Gravitational instantons; 10 Anti-self-dual conformal structures; Appendix A: Manifolds and Topology; Appendix B: Complex analysis; Appendix C: Overdetermined PDEs; Index

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