  We provide a framework for extensions of Lie algebroids, including
non-abelian extensions and Lie algebroids over different bases. Our approach
involves Ehresmann connections, which allows straight generalizations of
classical constructions. We exhibit a filtration in cohomology and explain the
associated spectral sequence. We also give a description of the groupoid
integrating an extension in case a complete connection can be fixed. The
problem of integrability is also studied.
