A Fast Trip Through the Classical Theory.- Motions in Plane Geometry and the 3-dimensional Brieskorn Manifolds.- 3-dimensional Lie Groups and Surface Singularities.- Within the Realm of the General Index Theorem.- On the Geometry and Topology of Quadrics in ??n.- Real Singularities and Complex Geometry.- Real Singularities with a Milnor Fibration.- Real Singularities and Open Book Decompositions of the 3-sphere.