Much progress has been made in recent years in understanding the complex physics of polarized radiation in the sun and stars. This physics includes vector radiative transfer and spectral line formation in the presence of magnetic fields, scattering theory and coherence effects, partial redistribution and turbulent magnetic fields, numerical techniques and Stokes inversion, as well as concepts for polarimetric imaging with a precision limited only by photon statistics. The present volume gives a comprehensive and up-to-date account of this rapidly evolving field of science.