This lecture by the instructor covers the concept of topological waves for robust signal processing applications. It explores the design paradigm of topological waves systems that resist continuous perturbations, focusing on topological insulators, edge states, and the importance of chiral symmetry. The lecture delves into the theory behind topological invariants, the topology of Bloch band structures, and the implementation of topological filters. Experimental validations and examples in photonics and acoustics are discussed, showcasing the robustness and unique properties of topological wave systems.