Explore the fundamental concepts of p-adic geometry in this comprehensive lecture focusing on adic and perfectoid spaces. Delve into the intricate world of p-adic numbers and their geometric applications as presented by Judith Ludwig at the Hausdorff Center for Mathematics. Gain insights into the theory of adic spaces and their perfectoid counterparts, understanding their significance in modern algebraic geometry and number theory. Discover how these advanced mathematical structures provide powerful tools for solving complex problems in various areas of mathematics.