  We extend the notion of connection in order to be able to study singular
geometric structures, namely, we consider a notion of connection on a Lie
algebroid which is a natural extension of the usual concept of connection.
Using connections, we are able to define holonomy of the orbit foliation of a
Lie algebroid and prove a stability theorem. We also introduce secondary or
exotic characteristic classes that generalize the modular class of a Lie
algebroid.
