In the next two talks, I will discuss another well-known problem which was very nicely formulated by Mark Kac as "Can one hear the shape of a drum?", and its solution, for arithmetic quotients of symmetric spaces, obtained in a joint work (in Publ Math IHES) with Andrei Rapinchuk. For the solution, we introduced a notion of "weak commensurability" of arithmetic, and more general Zariski-dense, subgroups and derive very strong consequences of weak commensurability.