Most stars appear to show some degree of magnetic activity. Varying magnetic fields show up in the familiar sun-spot cycle and in similar activity in other cool stars. Many hot stars carry steady magnetic fields stronger than the average solar field and are well described as oblique rotators. A similar model is applicable to the rapidly rotating, enormously dense neutron stars with their far stronger fields, observed as radio and X-ray pulsars. Galactic magnetic fields may play a crucial role in star formation, and in the spectacular behaviour in galactic nuclei. Cosmical magnetism in general is a rapidly developing field, and this book has grown out of the lifelong work of an outstanding researcher in the area. An authoritative account with broad astronomical scope, its thorough, careful and well-argued approach makes it a fine addition to the professional literature. Most of the important topics are treated in mathematical depth with references to other relevant literature. Some of the studies, especially those on accretion discs, dynamos, and winds, are applicable to galaxies and galactic nuclei. This book is sure to become an invaluable professional reference and guide to current thinking in the field. It will be of particular interest to graduate students, for whom it shows how the area has developed and indicates the many challenging research problems, some of which may soon yield their secrets to the emerging supercomputers.