Cosmic Magnetic Fields: from Stars and Galaxies to the Primordial
  Universe
  Most of the baryonic matter in the Universe is permeated by magnetic fields
which affect many, if not most, of astrophysical phenomena both, in compact
sources and in diffuse gas. Recent years have been marked by a worldwide surge
of interest in the astrophysical magnetic fields, their origin, and their
influence on the formation and evolution of astrophysical objects (stars,
galaxies, cooling flows). This growing interest is in part due to the fact that
it has become possible to trace magnetic fields in molecular clouds, over vast
extensions of the Milky Way and to study extragalactic magnetic fields,
including fields in clusters of galaxies. With the combination of various
techniques, such as Zeeman and Faraday rotation measurements with synchrotron
and aligned grain polarimetry, it is now possible to undertake quantitative
observational studies of magnetic fields, the results of which can be compared
with high resolution dynamo and MHD turbulence simulations. This brings the
field to a new stage.
  In this paper, I will briefly review the importance of the cosmic magnetic
fields both from a theoretical and from an observational perspective, focusing
on their role in stellar and compact objects, in the interstellar medium and
star formation regions, and in galaxies, clusters of galaxies, and the
primordial Universe.
