Is it permissible, in Sharia, to demand compensation from my brother if he broke my glasses by sitting on the table where I had placed them, and what is the Sharia ruling on this matter?

You have the right to claim compensation from whoever damaged your glasses or any of your property, whether intentionally or by mistake, because intention and mistake are the same in damaging people's property. Whoever damages something is obligated to pay its value or provide its equivalent, unless you forgive and pardon, which is closer to piety. Allah Almighty said: "And the retribution for an evil deed is an evil deed like it; but whoever pardons and makes reconciliation - his reward is due from Allah. Indeed, He does not like wrongdoers."