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This book is an extensive monograph on Sasakian manifolds, focusing on the intricate relationship between K er and Sasakian geometries. The subject is introduced by discussion of several background topics, including the theory of Riemannian foliations, compact complex and K er orbifolds, and the existence and obstruction theory of K er-Einstein metrics on complex compact orbifolds. There is then a discussion of contact and almost contact structures in the Riemannian setting, in which compact quasi-regular Sasakian manifolds emerge as algebraic objects. There is an extensive discussion of the...