Explore topological clustering of multilayer networks in this 51-minute lecture by Yulia Gel. Delve into a new approach for grouping nodes based on the shape similarity of their local neighborhoods at various resolution scales. Learn how persistence diagrams quantify these shapes and discover the applications of single linkage and k-means forms of topological clustering. Understand how this method accounts for heterogeneous higher-order properties of node interactions within and between network layers. Examine the clustering stability guarantees derived from casting topological k-means into an empirical risk minimization framework. Apply these concepts to real-world examples, including climate-insurance and COVID-19 data. Gain insights into the utility of multilayer networks in modeling interdependent systems such as critical infrastructures, human brain connectome, and socio-environmental ecosystems.