Explore harmonic maps between surfaces and Teichmüller theory in this lecture by Michael Wolf, part of the Geometry, Groups and Dynamics program at the International Centre for Theoretical Sciences. Delve into the fundamentals of harmonic maps, energy functionals, and their applications in surface geometry. Examine the Hopf differential and its relationship to harmonic maps, and gain insights into the structure of Teichmüller space. Learn how these concepts connect to partial differential equations and geometric analysis. Engage with examples, remarks, and a comprehensive overview of the topic, concluding with a perspective on Teichmüller space and a Q&A session.