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Introduction ARLAN RAMSAY AND JEAN RENAULT ix Groupoids: Unifying internal and external symmetry. A tour through some examples ALAN WEINSTEIN 1 A primer for the Brauer group of a groupoid DANA P. WILLIAMS 21 Amenable groupoids CLAIRE ANANTHARAMAN AND JEAN RENAULT 35 The role of groupoids in classification theory: A new approach. The UHF algebra case GIULIO DELLA ROCCA AND MASAMICHI TAKESAKI 47 Bundles over groupoids PAUL S. MUHLY 67 Groupoids and foliations ANDRE HAEFLIGER 83 Etale groupoids, derived categories, and operations IEKE MOERDIJK 101 The analytic index for proper, Lie groupoid actions ALAN L. T. PATERSON 115 Groupoid C*-algebras and operator K-theory PIERRE-YVES LE GALL 137 Groupoids of manifolds with corners and index theory BERTRAND MONTHUBERT 147 Quantization of Poisson algebras associated to Lie algebroids N. P. LANDSMAN AND B. RAMAZAN 159