Title: Revisiting Lie integrability by quadratures from a geometric perspective,
Abstract: After a short review of the classical Lie theorem, a finite dimensional Lie
algebra of vector fields is considered and the most general conditions under
which the integral curves of one of the fields can be obtained by quadratures
in a prescribed way will be discussed, determining also the number of
quadratures needed to integrate the system. The theory will be illustrated with
examples andbn an extension of the theorem where the Lie algebras are replaced
by some distributions will also be presented.