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This volume contains a series of original research articles on global differential geometry and global analysis. Topics discussed include generalized Cayley surfaces, affine and Euclidean completeness, transversal curvature and tautness for Riemannian foliations and much more.

The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Backlund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.