About the Book: This book offers a highly accessible introduction to singularity theory through the lens of differential geometry of curves and surfaces. Written by three experts, it covers singularities, recognition theorems, and applications to geometry and topology, focusing on plane curves and surfaces in Euclidean 3-space. Key topics include singular curvature and a generalized Gauss–Bonnet theorem for surfaces with singularities, as well as Riemannian manifolds with singularities. Rich in examples, figures, and exercises, the book provides both theory and practical insight, making it ideal for students and researchers seeking a unique perspective on singularities in differential geometry.