This text records the proceedings of the IUTAM Symposium held in Aachen in 1997. It reviews theories based on asymptotic expansions and gives an insight into new computational methods. Some applications of these methods demonstrate their capability, for example the analysis of core structures with axial variation, the description of the interaction of filaments with a solid body and of sound generation by vortex rings, the theoretical approach to the reduction of drag by manipulating vortex structures in shear layers, the numerical simulation of merging vortex rings and of bubble-type vortex breakdown in a tube, and investigations of vortex flows in aircraft and helicopter applications. The articles comprise a wide variety of fundamental investigations and of advanced engineering applications. The book summarizes the state of the art and also communicates recent results of specific flow problems. It addresses the large readership experienced in the field of vortex dynamics.