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This memoir is part of the author's `Habilitation \`a Diriger des Recherches'(HDR) dossier: it summarizes some of his researches after his PhD thesis.  (The HDR diploma is general requirement for many purposes [e.g., supervisingPhD students] within the French academic system.)

Quelques contributions \`a la th\'eorie de l'action de SL(2,R) sur les espaces de modules de surfaces plates