  Let $G$ be a free group of rank $n$ and $H\subset G$ its subgroup of finite
index. Then $H$ is also a free group and the rank $m$ of $H$ is determined by
Schreier's formula $m-1=(n-1)\cdot|G:H|.$
  Any subalgebra of a free Lie algebra is also free. But a straightforward
analogue of Schreier's formula for free Lie algebras does not exist, because
any subalgebra of finite codimension has an infinite number of generators.
  But the appropriate Schreier's formula for free Lie algebras exists in terms
of formal power series. There exists also a version in terms of exponential
generating functions. This is a survey on how these formulas are applied to
study 1) growth of finitely generated Lie algebras and groups and 2) the
codimension growth of varieties of Lie algebras. First, these formulae allow to
specify explicit formulas for generating functions of respective types for free
solvable (or more generally, polynilpotent) Lie algebras. Second, these
explicit formulas for generating functions are used to derive asymptotic for
these two types of the growth. These results can be viewed as analogues of the
Witt formula for free Lie algebras and groups. In case of Lie algebras, we
obtain two scales for respective types of growth. We also shortly mention the
situation on growth for other types of linear algebras.
