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The topics of the course, related to recent astrophysical and geophysical problems, is also very attractive to applied mathematicians. Sophisticated mathematical approaches applying wide spectra of numerical as well as analytic and asymptotic methods are necessary for successful and effective solutions of those physical problems. The first goal of the course is to motivate mathematicians to solve complex physical problems. Therefore, the course indicates an attractiveness and practical usefulness of topics related to the magnetic fields generation of cosmic bodies, in particular of the Earth and Sun. Understanding and the ability to predict the time behaviour of the last two fields has also enormous practical significance, and it is not yet solved. The second goal is to show how various branches of mathematics are indispensable in solving the problems of Convection and Dynamo Theory in astro- and geophysics. The 3rd goal is to introduce the basic physical background for the topics with emphasis on mathematical expression of this physics, i.e. to underline the correspondence between the physics and mathematics of the topics.