Special geometries as well as the relation between curvature and topology have always been of interest to differential geometers. More recently, these topics have turned out to be of use in physical problems related to string theory as well. This volume provides a unique and thorough survey on the latest developments on Riemannian geometry, special geometrical structures on manifolds, and their interactions with other fields such as mathematical physics, complex analysis, and algebraic geometry. This volume presents ten papers written by participants of the 'Short Program on Riemannian Geometry', a workshop held at the CRM in Montreal in 2004. It will be a valuable reference for graduate students and research mathematicians alike.