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.

M. Gromov, Almost flat manifolds, J. Differential Geometry 13 (1978) 231241 online at http://seven.ihes.fr/~gromov/PDF/3[20].pdf 


The book "Gromov's almost flat manifolds" by Buser and Karcher is a nice exposition of Gromov's result. 

