This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems — classical and quantum — are considered.Contents:Advances in Analytical Methods:Nevanlinna Theory and Difference Equations of Painlevé Type (M J Ablowitz & R Halburd)Monodromy Transform Approach to Solution of Some Field Equations in General Relativity and String Theory (G A Alekseev)Nonlinear Sigma Model on Curved Surfaces: Energy and Anholonomy (R Balakrishnan)Advances in Symmetry Properties, Hamiltonian and Group Theoretical Methods:Möbius Symmetry, KP Symmetry Constraints and Calogero-Moser System (L V Bogdanov & B G Konopelchenko)KP, Modified KP, Discrete KP, Constrained KP, and q-KP (L A Dickey)On Lie Group Classification of Second-Order Ordinary Difference Equations (V Dorodnitsyn et al.)Near Integrable Systems and Perturbative Methods:Oscillatory Instability and Supercritical Dynamics of Damped-Driven Nonlinear Schrödinger Solitons (N V Alexeeva et al.)On the Existence of Radial Sine-Gordon Breathers (G L Alfimov et al.)Role of High Harmonics in Gap Soliton Evolution (G Alfimov & V V Konotop)Applications in Science and Technology:Coupled Modified Kadomtsev-Petviashvili Equations in a Higher Order Gradient Elastic Medium (C Babaoglu & S Erbay)Nonlinear Dynamics in Hydrogen Bonded Molecules (M Barthès et al.)The Window Josephson Junction: A Coupled Linear-Nonlinear System (A Benabdallah & J G Caputo)and other papersReadership: Physicists and mathematicians.Key Features:Reflects recent formidable advances in, and presents a new picture of wave turbulence using a common mathematical modelExperimental and theoretical viewpoints on enhancing the predictive and descriptive powers of wave turbulence