Explore the intricacies of Nijenhuis geometry in this advanced mathematics lecture delivered as part of the Thematic Programme on "Geometry beyond Riemann: Curvature and Rigidity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into complex mathematical concepts and theories as the speaker builds upon the foundations laid in the previous talk, offering deeper insights into this specialized field of geometry. Gain a comprehensive understanding of the subject matter through a 49-minute presentation that challenges and expands conventional perspectives on geometric structures and their properties.