This book examines and explores Jacques Lacan controversial topologisation of psychoanalysis, and seeks to persuade the reader that this enterprise was necessary and important. In providing both an introduction to a fundamental component of Lacan theories, as well as readings of texts that have been largely ignored, it provides a thorough critical interpretation of his work. Will Greenshields argues that Lacan achieved his most pedagogically clear and successful presentations of his most essential and notoriously complex concepts – such as structure, the subject and the real – through the deployment of topology. The book will help readers to better understand Lacan, and also those concepts that have become prevalent in various intellectual discourses such as contemporary continental philosophy, politics and the study of ideology, and literary or cultural criticism.