This book springs from the programme Quantized Vortex Dynamics and Sup-—fluid Turbulence held at the Isaac Newton Institute for Mathematical Sciences (University of Cambridge) in August 2000. What motivated the programme was the recognition that two recent developments have moved the study of qu- tized vorticity, traditionally carried out within the low-temperature physics and condensed-matter physics communities, into a new era. The first development is the increasing contact with classical fluid dynamics and its ideas and methods. For example, some current experiments with - lium II now deal with very classical issues, such as the measurement of velocity spectra and turbulence decay rates. The evidence from these experiments and many others is that superfluid turbulence and classical turbulence share many features. The challenge is now to explain these similarities and explore the time scales and length scales over which they hold true. The observed classical aspects have also attracted attention to the role played by the flow of the normal fluid, which was somewhat neglected in the past because of the lack of direct flow visualization. Increased computing power is also making it possible to study the coupled motion of superfluid vortices and normal fluids. Another contact with classical physics arises through the interest in the study of superfluid vortex - connections. Reconnections have been studied for some time in the contexts of classical fluid dynamics and magneto-hydrodynamics (MHD), and it is useful to learn from the experience acquired in other fields.