This volume gives an overview of the recent ideas in studies of nonlinear waves and pattern formation in physical, chemical and biological active media. The papers deal with spatio-temporal growth of bacterial colonies, pattern formation and pattern recognition, pattern selection in Benard-Marangoni convection, chemical turbulence and parametric resonance of vortices in the Belousov-Zhabotinsky reaction, oscillatory electrodissolution of metals, discretely-coupled electronic arrays, optical space-time complexity, spiral waves in nematic liquid crystals and several approaches to control chaos. The stability of hexagonal patterns with some asymmetries are analyzed, both for convective systems and Turing structures. Some other lectures are devoted to the important question of the topology of defects in superfluids, convective and reaction-diffusion systems.