  We present the (Lascar) Galois group of any countable theory as a quotient of
a compact Polish group by an $F_\sigma$ normal subgroup: in general, as a
topological group, and under NIP, also in terms of Borel cardinality. This
allows us to obtain similar results for arbitrary strong types defined on a
single complete type over $\emptyset$. As an easy conclusion of our main
theorem, we get the main result from our recent paper joint with Andand Pillay,
which says that for any strong type defined on a single complete type over
$\emptyset$, smoothness is equivalent to type-definability.
  We also explain how similar results are obtained in the case of bounded
quotients of type-definable groups. This gives us a generalization of a former
result from the aforementioned paper about bounded quotients of type-definable
subgroups of definable groups.
