The present report deals with the basic facts of extra-galactic astronomy. It should be noted that a true picture of the outer stellar systems (galaxies) was formed in astronomy only about forty years ago. As a result, most basic problems concerning the outer galaxies remain unresolved. We, therefore, formulate in the present report a number of problems which, in our view, seem to constitute the most essential points in the further exploration of the outer galaxies. We shall try to keep as close to the facts as possible and handle, primarily, those problems the solution of which may seem possible in the near future with the means available to us.