This lecture covers the multiplication of M matrices and conversion into S matrix for two-cascaded systems, including free space propagation. It also discusses the response obtained as a geometric progression and provides examples of beamsplitter, perfect mirror, and single dielectric boundary. The lecture further explores propagation examples, such as transmission through a slab and quarter-wave film, as well as technology considerations like ion beam sputtering and atomic layer deposition. Additionally, it delves into off-axis propagation in layered media, explaining Fresnel coefficients and providing examples of single boundaries. The content is presented by the instructor Olivier J.F. Martin.