This volume addresses the philosophical, epistemological and interdisciplinary aspects of the link between psychoanalysis and topology. Looking at the historical developments of psychoanalytic theory, one can hardly overlook the significant presence of architectonic and geometrical references that traverse Freud's writings. Lacan's return to Freud made a decisive step in taking these metaphors seriously and engaged with the mathematical correspondence of Freud's topological models. He thereby intensified the link with topology, which obtained an important didactic and conceptual value. The contributions highlight the ongoing relevance of this "topological turn" in psychoanalysis by exploring both concrete topological objects and outline the philosophical framework that supports the relation of psychoanalysis to topology.