This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences. Contents: Volume 1: Celestial MechanicsHomoclinic TangenciesSingular PerturbationsStochastic SystemsSymmetryTopological Methods and Conley IndexDelay EquationsGeometric DynamicsHyperbolic Conservation LawsHyperbolic Wave EquationsHysteresisLarge DomainsLattice Dynamical SystemsMicrostructureNonlinear Functional AnalysisVariational MethodsViscosity SolutionsGlobal Attractors and LimitsNonautonomous AttractorsOrder-Preserving Dynamical SystemsQualitative Theory of Parabolic EquationsStability of Fronts and Pulses Volume 2: Computer Algebra ToolsControl and OptimizationDynamics and AlgorithmsExponentially Small PhenomenaGeometric IntegratorsNumerical Ergodic TheoryNumerics of DynamicsChemistryChemotaxis, Cross-Diffusion, and Blow-UpIndustrial ApplicationsMechanicsModels in Biology, Medicine, and PhysiologyMolecular ModellingPatternsSemiconductorsSteady Water WavesUnsteady Hydrodynamic WavesDelay EquationsNumericsOrdinary Differential EquationsPartial Differential Equations Keywords:Dynamical Systems;Infinite Dimensions;Global Attractors;Stability;Computational Aspects;Celestial Mechanics;Homoclinic Tangencies;Singular Perturbations;Stochastic Systems;Conley Index;Delay Equations;Hyperbolic Wave Equations;Viscosity Solutions;Control and Optimization;Geometric Integrators;Numerical Ergodic Theory;Molecular Modelling;Patterns;Steady Water Waves