abstract: We study representations of the Atiyah algebroid of a line bundle, and establish some relation with flat logarithmic connections. Thus we are able to formulate in a natural way established properties of logarithmic connections. As an application, we give a "functorial" definition of the residue of a logarithmic connection, and show that Deligne's Riemann-Hilbert correspondence between representations of the fundamental group and flat meromorphic bundles follows directly from the second theorem of Lie for Lie algebroids/groupoids.