The first volume starts with a historical overview of nonlinear dynamics from Poincaré to the present day and touches topics like attractors, nonlinear oscillators and waves, turbulence, pattern formation, and dynamics of structures in nonequilibrium dissipative media.

I Nonlinear Dynamics: From Poincaré to the Present Day.- Nonlinear Dynamics: Poincaré and Mandelstam.- Attractors.- From Nonlinear Oscillations to Nonlinear Waves.- Nonlinear Dynamics and Turbulence.- Pattern Formation and Dynamics of Two-Dimensional Structures in Non-Equilibrium Dissipative Media.- II Structures.- Bistabilities, Instabilities and Chaos in Passive Nonlinear Optical Systems.- Dynamics of Defects and Onset of Spatial Chaos in One-Dimensional Systems.- Self-Organization Phenomena in Laser Thermochemistry.- Thermal-Diffusion Autosolitons in Semiconductor and Gas Plasmas.- The Wave-Turbulent Dynamo.- Criteria of the Existence of Moving Structures in Two-Component Reaction-Diffusion Systems.- Spatio-Temporal Structures in Opto-Electronic Devices.- Multiple Array Processors for Two-Dimensional Nonequilibrium Media Computer Simulation.- Laser-Induced Instabilities and Phase Transitions on the Surfaces of Solids with the Formation of the Ordered Structures.- Stimulated Scattering and Surface Structures.- Distributed Wave Collapse in the Nonlinear Schrödinger Equation.- Index of Contributors.