Table of Contents

Planar Curves and Singular Points; Singularities of Surfaces; Proof of Criteria for Singularities; Application of Criteria for Singularities; Local Differential Geometry of Surfaces with Singularities; Gauss–Bonnet Type Formulas and Applications; Flat Surfaces; Proof of the Criterion for Swallowtails; Coherent Tangent Bundles; Contact Structures and Wave Fronts; Appendices: The Division Lemma; Topics on Cusps; A Criterion for 4/3-cusps; Proof of the Criterion for Whitney Cusps; A Zakalyukin-Type Lemma; A Formula for Singular Curvature; Geometry of Cross Caps;