Prasad’s Volume Formula and Its Applications

After giving brief historical context, we present Prasad’s famous formula for the volume of quotients of semisimple groups over local fields by arithmetic subgroups, faithfully to the original article [Volumes of S-arithmetic quotients of semisimple groups. Publ. Math., Inst. Hautes Étud. Sci., 69:91–117, 1989]. We then survey the applications it has found in geometry, group theory, and arithmetic over the last four decades.