  These notes cover the lectures of the first named author at 2021 IHES Summer
School on "Enumerative Geometry, Physics and Representation Theory" with
additional details and references. They cover the definition of
Khovanov-Rozansky triply graded homology, its basic properties and recent
advances, as well as three algebro-geometric models for link homology: braid
varieties, Hilbert schemes of singular curves and affine Springer fibers, and
Hilbert schemes of points on the plane.
