This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.

Introduction * N-Vortices in the Plane * Domains with Boundaries * Vortex Motion on a Sphere * Geometric Phases * Statistical Point Vortex Theories * Vortex Patch Models * Vortex Filament Models * References * Index