This lecture is part of the ICTP-SAIFR School on the Origins of Life, Behavior and Cognition (March 10-21, 2025), featuring Manuel Schottdorf from the University of Delaware exploring the topology and geometry of perception and knowledge in his second class session. Delve into the mathematical frameworks that help explain how organisms perceive their environment and organize knowledge during this 75-minute presentation. The lecture is part of a comprehensive program examining fundamental questions at the intersection of cognitive science, biology, and mathematics.