Although natural phenomena can be described by a few simple and symmetric basic laws they exhibit an astounding variety of behaviours. This can be explained by a process known as symmetry breaking, which can cause an ordered state to form with topological defects. The dynamics of further evolution are determined to a large extent by the dynamics of such defects. This book covers the structure and dynamics of vortices in a variety of nonlinear field models with spontaneously broken symmetry. Point vortices or vortex lines can correspond, depending on the physical setting, to quantized vortices in superfluids or superconductors, dislocations in non- equilibrium patterns, rotating spiral waves, disclinations in liquid crystals, singularities in optical fields or strings in relativistic field theories. This book is unique in considering vortices in these different settings, but also emphasizes the analytical methods that allow an understanding of the common theoretical structure underlying defect dynamics.