Why did the Sharia establish fixed punishments (Hudud) for murder, adultery, and theft, but not for usury, even though its harm extends to the entire Muslim society? And how does a person who wishes to purify himself from a major sin he has committed go about doing so?

Allah has legislated Hudud (prescribed punishments) for crimes whose motivations are strong within the human soul, or which lead to the loss of religion and the corruption of worldly life. Usury (riba) does not necessitate a Hadd punishment because souls naturally recoil from it willingly, and because its effects are not like those of apostasy, highway robbery (hirabah), false accusation (qadhf), or theft. Nevertheless, usury is a grave crime, and even if it does not have a Hadd punishment, it is subject to a discretionary punishment (ta'zir) determined by the ruler as he deems deterrent. A person purifies himself from this grave sin through sincere repentance (tawbah nasuh).