Full paper in PDF format:
$%N. J. Kalton, The nonlinear geometry of Banach spaces, Rev. Mat. Complut. 21 (2008), no. 1,7–60.%$

We survey some of the recent developments in the nonlinear theory of Banach spaces, with emphasis on problems of Lipschitz and uniform homeomorphism and uniform and coarse embeddings of metric spaces.

Key words: Banach space, nonlinear, Lipschitz, uniform homeomorphism, coarse embedding.
2000 Mathematics Subject Classification: 46B25, 46T99.