Chemical patterns supported by nonlinear reaction-transport systems are not restricted to propagating waves. Standing, oscillating, chaotic and multiply periodic phenomena may also occur. This volume is concerned with chemical waves mechanics arising from reaction-transport systems. It demonstrates that, as with the free particle in quantum mechanics, certain simple elements can serve as organizing tools for the understanding of the complex phenomena treated. The observed variety of waves and patterns is derived from the analysis of the mathematical structures implied by the simple elements.