"The present book has been enriched by including, in the Notes of each chapter, other aspects and studies on the topics in questions and by providing a wide list of references. The book will be a helpful tool for researchers interested in the field and in particular, in the study of the differential geometry of singular submanifolds of Euclidean and Minkowski spaces."European Mathematical SocietyDifferential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.