TITLE: Reference request for an early theorem of Gromov
QUESTION [5 upvotes]: In his talk Misha Gromov- How does he do it, Jeff Cheeger mentions a theorem of Gromov proved sometime in the early 70's. Theorem: Every manifold admitting a sequence of metrics such that the diameter and curvature go to zero is finitely covered by a nilmanifold.
Further, he says that the proof is not easy even today; something usually associated with Gromov! 
It would be great to read the original paper, and even better if some book contains it. Please help me find them. Thanks.

REPLY [7 votes]: The book "Gromov's almost flat manifolds" by Buser and Karcher is a nice exposition of Gromov's result.