  We study systems involving vector bundles and logarithmic connections on
Riemann surfaces and linear algebra data linking their residues. This
generalizes representations of deformed preprojective algebras. Our main result
is the existence of a monodromy functor from such systems to representations of
a multiplicative preprojective algebra. As a corollary, we prove that the
multiplicative preprojective algebra associated to a Dynkin quiver is
isomorphic to the usual preprojective algebra.
