  A new construction of a universal connection was given in \cite{BHS}. The
main aim here is to explain this construction. A theorem of Atiyah and Weil
says that a holomorphic vector bundle $E$ over a compact Riemann surface admits
a holomorphic connection if and only if the degree of every direct summand of
$E$ is degree. In \cite{AB}, this criterion was generalized to principal
bundles on compact Riemann surfaces. This criterion for principal bundles is
also explained.
