Local Rigidity of group actions: Past, Present, Future

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This survey aims to cover the motivation for and history of the study of local rigidity of group actions. There is a particularly detailed discussion of recent results, including outlines of some proofs. The article ends with a large number of conjectures and open questions and aims to point to interesting directions for future research. {\em To Anatole Katok on the occasion of his 60th birthday.}
Survey article, final version for publication, see also http://mypage.iu.edu/~fisherdm/

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