Description This edition of a classic review presents some topics in hydromagnetic dynamo theory in the astrophysical context of large magnetic Reynolds number: Criteria are defined for field generation in a state of near-complete freezing in. An account is given of certain qualitative aspects of a turbulent dynamo operating through nonuniform rotation of a conducting medium subject to random motions with helicity. Such dynamos might be at work in planetary cores, stellar envelopes, galaxies and the gaseous accretion disks around X-Ray sources. The concepts of stochasticity and strange attractors in a magnetic dynamo are explained in a qualitative interpretation is offered for the occasional prolonged interruptions of the solar cycle, such as the Maunder minimum.