  Almost Lie algebroids are generalizations of Lie algebroids, when the
Jacobiator is not necessary null. A simple example is given, for which a Lie
algebroid bracket or a Courant bundle is not possible for the given anchor, but
a natural extension of the bundle and the new anchor allows a Lie algebroid
bracket. A cohomology and related characteristic classes of an almost Lie
algebroid are also constructed. We prove that these characteristic classes are
all pull-backs of the characteristic classes of the base space, as in the case
of a Lie algebroid.
