  The objectives of this paper is to give a systematic investigation of
extension theory of loops. A loop extension is (left, right or middle) nuclear,
if the kernel of the extension consists of elements associating (from left,
right or middle) with all elements of the loop. It turns out that the natural
non-associative generalizations of the Schreier's theory of group extensions
can be characterized by different types of nuclear properties. Our loop
constructions are illustrated by rich families of examples in important loop
classes.
