Explore the intricacies of Hermitian K-theory in this lecture from the Hausdorff Trimester Program Topology Workshop. Delve into Voevodsky's filtration of the motivic stable homotopy category and its application to various motivic spectra. Discover the groundbreaking work on computing the slices of Hermitian K-theory, also known as higher Grothendieck-Witt theory. Gain insights into the natural approach to Milnor's conjecture on quadratic forms. Cover topics such as smooth schemes, periodicity, geometric P2 spectra, presheaves, almond toffee theory, topology, differential topology, forcible schemes, LDH topology, classical sphere, triangulation, filter, first law, and motivation ecology.