Explore new foundations for analytic geometry in this comprehensive lecture by Peter Scholze from MPIM Bonn, delivered at the Institut des Hautes Etudes Scientifiques (IHES). Delve into four key areas over the course of nearly two hours: light condensed abelian groups, analytic rings, analytic stacks, and relevant examples. Gain insights into cutting-edge mathematical concepts and their applications in this advanced exploration of analytic geometry.