The paper has a form of a talk on the given topic. It consists of three
parts.
  The first part of the paper contains main notions, the second one is devoted
to logical geometry, the third part describes types and isotypeness. The
problems are distributed in the corresponding parts. The whole material
oriented towards universal algebraic geometry (UAG), i.e., geometry in an
arbitrary variety of algebras $\Theta$. We consider logical geometry (LG) as a
part of UAG. This theory is strongly influenced by model theory and ideas of
A.Tarski and A.I.Malcev