In this lecture I will argue that elasticity theory needs to be fundamentally changed in order to deal with amorphous solids. In a recent paper [Phys. Rev. E 104, 024904] we showed that mechanical  strains in amorphous solids are screened via the formation of plastic events that are typically quadrupolar in nature.  At low densities of quadrupoles the screening effect is reminiscent of the role of dipoles in dielectrics, while the effect at high density has no immediate electrostatic analog, and is expected to change qualitatively the mechanical response, as seen for example in the displacement field. The phenomenon is akin to a Kosterlitz-Thouless transition as will be explained in this lecture. I will show that high-density screening results in undulating displacement fields that strictly deviate from elasticity theory. Theoretical analysis, experimental measurements and numerical simulations of frictional granular amorphous assemblies are in agreement with each other and provide a strong support for the theory.