The past 20 years have shown a rapid growth in the theoretical understanding, useful applications and widespread acceptance of multigrid in the applied sciences, and new tasks continue to arise that are better addressed from a special multigrid point of view. These developments have served to make multigrid one of the key techniques in modern computing methods. Most prominent among the new issues are parallel computing and adaptive computations. Multigrid methods also have considerable impact on computational fluid dynamics. This influence is reflected in the present, carefully screened...