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.
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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. 

