This volume contains two articles. Both deal with generalizations of Michael Harris' and Richard Taylor's work on the cohomology of P.E.L. type Shimura varieties of signature \((1,n1)\) and on the cohomology of LubinTate spaces. They are based on the work of Robert Kottwitz on those varieties in the general signature case, and on the work of Michael Rapoport and Thomas Zink on moduli spaces of \(p\)divisible groups generalizing the one of LubinTate and Drinfeld. In the first article it is proved that the \(\ell\)adique étale cohomology of some of those "supersingular" moduli spaces of \(p\)divisible groups realizes some cases of local Langlands correspondences. For this the author establishes a formula linking the cohomology of those spaces to the one of the "supersingular" locus of a Shimura variety. Then he proves that the supercuspidal part of the cohomology of those varieties is completely contained in the one of the "supersingular" locus. The second article links the cohomology of a Newton stratum of the Shimura variety, for example the "supersingular" stratum, to the cohomology of the attached local moduli space of \(p\)divisible groups and to the cohomology of some global varieties in positive characteristic named Igusa varieties that generalize the classical Igusa curves attached to modular curves. The book is suitable for graduate students and research mathematicians interested in number theory and algebraic geometry. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in number theory and algebraic geometry. Table of Contents L. Fargues. Cohomologie des espaces de modules de groupes \(p\)divisibles et correspondances de Langlands locales  Introduction
 Variétés de Shimura de type P.E.L. non ramifiées
 Espaces de RapoportZink
 Uniformisation des variétés de Shimura de type P.E.L.
 Une suite spectrale de HochschildSerre pour l'uniformisation de RapoportZink
 Formule de Lefschetz sur la fibre spéciale
 Formule de Lefschetz sur la fibre générique
 Contribution de la cohomologie de la strate basique
 Application à la cohomologie des espaces RapoportZink de type E.L. et P.E.L.
 Appendices
 Références
E. Mantovan. On Certain Unitary Shimura Varieties  Introduction
 Preliminaries
 Igusa varieties
 A system of covers of the Newton polygon strata
 Group action on cohomology
 Formally lifting to characteristic zero
 Shimura varieties with level structure at \(p\)
 The cohomology of Shimura varieties
 References
