Explore advanced concepts in polyhedral products through this graduate-level lecture delivered by Steven Amelotte from Carleton University at the Fields Institute. Delve into sophisticated mathematical structures and their applications in algebraic topology during this comprehensive 65-minute session. Build upon foundational knowledge from previous parts of the graduate school series to understand complex relationships between polyhedral complexes and their associated topological spaces. Examine theoretical frameworks, computational techniques, and current research developments in this specialized area of mathematics. Gain insights into how polyhedral products connect combinatorial geometry with algebraic topology, providing essential tools for advanced mathematical research and applications.