Supermembranes and Super Matrix Theory

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We review recent developments in the theory of supermembranes and their relation to matrix models.
Invited talk given at the 31-st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, September 2 - 6, 1997 (to appear in Fortschritte der Physik) and at the CERN Theory Division, December 3, 1997. Latex, 19 pp. Minor corrections

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