Topics of this course are related to recent astrophysical and geophysical problems strongly progressing in the last decades due to common interaction of four parts, namely, theory supported by physical principles, observations with measurements from space and ground, and computational simulations and laboratory experiments. The topics can be attractive also to applied mathematicians due to sophisticated mathematical approaches applying wide spectra of numerical as well as analytic and asymptotic methods which are necessary for successful and effective solutions of the attractive 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 field generation of cosmic bodies, in particular of the Earth and Sun. Understanding and the ability to predict the time behavior 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. The attention will be focused on two bases, (1) the Study of Convection Instabilities (in rotating fluids permeated by magnetic fields) with some models of Rotating Magnetoconvection, and (2) the Foundations of Magnetohydrodynamics with Dynamo Theory applied on Natural Dynamos. The mathematical approaches with convenient approximations based on physical understanding of details in Dynamo mechanisms will be presented. Significant advancement in comparison with 2016-course is planned.