Integrable systems
Introductory, reviews and general
Lecture notes
Babelon, A short introduction to classical and quantum integrable systems
Dunajski, Integrable systems
Dubrovin, Krichever, Novikov: Integrable systems, I
Dubrovin, Integrable systems and Riemann surfaces
Beisert, Introduction to integrability
Review collections
MIkhailov (ed.), Integrability
Kosmann-Schwarzbach, Grammaticos and Tamizhmani (eds), Integrability of nonlinear systems
Zakharov (ed), What is integrability ?
Conceptual and mathematical
MacCallum and Mikhailov, Algebraic theory of differential equations
Blaszak, Multi-Hamiltonian theory of dynamical systems
Hitchin, Segal and Ward, Integrable Systems:Twistors, Loop Groups, and Riemann Surfaces
Dunajski, Solitons, instantons and twistors
Natanzon, Complex Analysis, Riemann Surfaces and Integrable Systems
Mason, Nutku, Geometry and integrability
Classical (finite-dimensional)
Babelon, Bernard, Talon: Introduction to classical integrable systems
Audin, Spinning tops, a course on integrable systems
Cushman and Bates, Global aspects of classical integrable systems
Moser, Stable and random motions in dynamical systems
Meyer and Hall, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
Siegel and Moser, Lectures on celestial mechanics
Sternberg, Celestial mechanics, vols 1 and 2
KAM theory
Chiercia, Kolmogorov-Arnold-Moser (KAM) theory for finite and infinite dimensional systems
Fejoz, Introduction to KAM theory with a view to celestial mechanics
de la Llave, A tutorial on KAM theory
Lazutkin, KAM theory and semiclassical approximations to eigenfunctions
Garay and van Straten, KAM theory
Algebraic integrable systems
Donagi and Shaska (eds), Integrable systems and algebraic geometry, vols. 1 and 2
Vanhaecke, Integrable systems in the realm of algebraic geometry
Infinite-dimensional and quantum
Kuskin, Analysis of Hamiltonian PDEs
Kappeler & Poschel, KdV & KAM
Faddeev and Takhtajan, Hamiltonian methods in the theory of solitons
Harnad and Balogh, Tau functions and their applications
Miwa, Jimbo and Date, Solitons: Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras
Korepin, Bologiubov, Izergin, Quantum Inverse Scattering Method and Correlation Functions
Nonlinear waves and solitons
Ablowitz & Segur, Solitons and the Inverse Scattering Transform
Manakov, Novikov, Pitaevski, Zakharov, Theory of Solitons: The Inverse Scattering Method
Drazin & Johnson, Solitons
Hirota, The Direct Method in Soliton Theory
Johnson, A Modern Introduction to the Mathematical Theory of Water Waves
Jeffrey & Kawahara, Asymptotic methods in nonlinear wave theory