This paper gives a survey of the theories (Part I) and phenomena (Part II) of cosmic magnetism, extending from geomagnetism over solar and sunspot magnetism to stellar and interstellar magnetic fields. The theoretical treatment is purely classical and Maxwelliam. Most cosmic fluids, being highly ionized, are excellent conductors; this implies that the displacement current can always be neglected. The fundamental equations of hydromagnetism are the electromagnetic field equations together with the hydrodynamic equation, both containing coupling terms between magnetic field and motion. Among other theoretical developments, the “dynamo” theory which ascribes the cosmic magnetic fields to amplifying processes in the moving fluid is described and it is shown that it is well suited to represent the observed phenomena of the generation and maintenance of cosmic magnetic fields.