The emergence of coherent vortex structures is a characteristic feature of quasi-geostrophic or two-dimensional turbulence and because of their relevance to large-scale geophysical flows, the dynamics of these structures has been studied increasingly over the past decade. In the oceans and in the atmospheres vortices or eddies are abundant. For this reason, the study of isolated vortices in rotating fluids-including their dynamics, instability properties, mutual interaction behavior, and effects due to bottom topog raphy-is of fundamental interest for refined models of geostrophic turbulence and of the general oceanic and atmospheric circulations. Pro cesses of heat transfer, dispersion of biochemical components, and the transport of other physical properties are closely connected with coherent structures. The dynamics of two-dimensional vortices in homogeneous fluids is also a key problem in free shear flows. With or without background rotation, the main question concerns the stability of these vortices to three dimensional disturbances. In addition, two-dimensional vortices also play an important role in tokamak-confined plasmas as well as in astrophysical situations such as accretion discs of neutron stars. During the past decade, considerable insight has been gained in the