Explore the intricate world of universes in set theory and type theory through this illuminating 53-minute lecture presented at the Hausdorff Center for Mathematics. Delve into the fundamental concepts and advanced applications of universes as Bauer and Carneiro elucidate their significance in mathematical foundations. Gain insights into how these structures shape our understanding of set-theoretic and type-theoretic frameworks, and discover their implications for modern mathematics and logic. Engage with cutting-edge research and theoretical developments in this essential area of mathematical study.