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With new observations delineating the large-scale magnetic fields in galaxies and renewed interest in the influence of magnetic fields on star formation and on the collimation of jets this book provides a timely review of cosmic magnetohydrodynamics. The book has a broad sweep, from the theory of the Earth's dynamo through the magnetically dominated Solar corona to the magnetic fields of stars, galaxies quasars and the intergalactic plasma. Particular strong points are the magnetic fields of degenerate stars. Both white dwarfs and the fascinating evolution of neutron stars' magnetic fields are discussed in detail. The book is dedicated to Professor Leon Mestel who has seen the subject grow from its early days to its current flowering on the wealth of new observations described here. Stellar winds, cosmic rays, galactic dynamos, active galactic nuclei and black holes provide a wide range for both scientific imagination and precise deduction. Many of the creators of the subjects have contributed to this volume, which is vital reading for astronomy graduate students with magnetic interests as well as plasma physicists.