Ongoing studies in mathematical depth, and inferences from `helioseismological'' observations of the internal solar rotation have shown up the limitations in our knowledge of the solar interior and of our understanding of the solar dynamo, manifested in particular by the sunspot cycle, the Maunder minimum, and solar flares. This second edition retains the identical overall structure as the first edition, but is designed so as to be self-contained with the earlychapters presenting the basic physics and mathematics underlying cosmical magnetohydrodynamics, followed by studies of the specific applications appropriate for a book devoted to a central area in astrophysics.