Explore the emerging field of valuations on spaces of functions in this 51-minute lecture by Andrea Colesanti from the Hausdorff Center for Mathematics. Begin with an introduction to the theory of valuations on convex bodies, which serves as the foundation for studying corresponding functionals in an analytic setting. Delve into the concept of valuations on function spaces, gaining a comprehensive overview of this young research topic. Examine recent developments, focusing on classifications of valuations in two specific areas: the space of Lipschitz functions and the space of convex functions. Gain insights into this evolving mathematical field and its potential applications.