Varieties of linear algebras of polynomial growth

The paper is survey of results of investigations on varieties of linear algebras of polynomial growth. We give equivalent conditions of the polynomial codimension growth of a variety of associative algebras, Lie algebras, Leibniz algebras, Poisson algebras, Leibniz–Poisson algebras. It is shown that in the study of varieties of linear algebras of polynomial growth varieties of almost polynomial growth play an important role.