This paper provides an introduction to a number of astrophysics problems
related to strong magnetic fields. The first part deals with issues related to
atoms, condensed matter and high-energy processes in very strong magnetic
fields, and how these issues influence various aspects of neutron star
astrophysics. The second part deals with classical astrophysical effects of
magnetic fields: Even relatively "weak" fields can play a strong role in
various astrophysical problems, ranging from stars, accretion disks and
outflows, to the formation and merger of compact objects.Comment: 16 pages. To be published in The Strongest Magnetic Fields in the
Universe (Space Sciences Series of ISSI, Springer), Space Science Review