Long time existence and singularity formation for vortex sheets -- Computation of vortex sheet roll-up -- Vortex ring interaction by the vortex method -- Vortex stretching and the small-scale structure of turbulence -- Instability, vortex shedding, and numerical convergence -- On the validity of vortex methods for non smooth flows -- Computation of oscillatory solutions to hyperbolic differential equations using particle methods -- On measuring the accuracy of the vortex method: Using a random method to model stable and untable flow -- Very large vortex calculations in two dimensions -- The rapid evaluation of potential fields in three dimensions