This book investigates the fundamental properties and classifications of singular points on plane curves. The author, C. T. C. Wall, a seasoned educator, draws upon his experience teaching graduate-level courses to provide an introduction to the subject. The text synthesizes techniques from algebra, algebraic geometry, complex analysis, and topology, offering a novel perspective and including new results. It is designed for graduate students seeking to understand the intricacies of curve singularities.

The book is presented as an introductory text for graduate students, leveraging the author's teaching experience to synthesize various mathematical perspectives on plane curve singularities. It aims to provide a novel view of the subject, incorporating new results and serving as an entry point into related fields like algebraic geometry and complex analysis. The approach emphasizes the utility of complex numbers in understanding even basic singularities. The text is structured to offer a comprehensive yet accessible treatment for its intended audience.