  Polarization is a basic property of light and is fundamentally linked to the
internal geometry of a source of radiation. Polarimetry complements
photometric, spectroscopic, and imaging analyses of sources of radiation and
has made possible multiple astrophysical discoveries. In this article I review
(i) the physical basics of polarization: electromagnetic waves, photons, and
parameterizations; (ii) astrophysical sources of polarization: scattering,
synchrotron radiation, active media, and the Zeeman, Goldreich-Kylafis, and
Hanle effects, as well as interactions between polarization and matter (like
birefringence, Faraday rotation, or the Chandrasekhar-Fermi effect); (iii)
observational methodology: on-sky geometry, influence of atmosphere and
instrumental polarization, polarization statistics, and observational
techniques for radio, optical, and X/gamma wavelengths; and (iv) science cases
for astronomical polarimetry: solar and stellar physics, planetary system
bodies, interstellar matter, astrobiology, astronomical masers, pulsars,
galactic magnetic fields, gamma-ray bursts, active galactic nuclei, and cosmic
microwave background radiation.
