Explore the isoperimetric inequality for Hausdorff contents and compact metric spaces in Banach spaces, including infinite-dimensional ones, in this 54-minute lecture. Delve into the implications for systolic geometry, focusing on new types of systolic inequalities applicable to a broader range of non-simply connected Riemannian manifolds than Gromov's classical systolic inequality. Gain insights from the joint work of Alexander Nabutovsky, Y. Liokumovich, B. Lishak, and R. Rotman, presented by Nabutovsky for the Applied Algebraic Topology Network.