No Stone Unturned

This quest begins when you find an Unusual Gem.

Walkthrough
Speak to Vex at the Thieves' Guild about the gem and she will tell you that it is a Stone of Barenziah, but a single stone by itself is worthless. However there are 23 more stones, and together they are worth quite a bit.

Recover the Stones of Barenziah (24)
You will already have at least one of the stones by now, but below is a complete list:


 * 1) Ansilvund, in Eastmarch, contains a stone near where you encounter Fjori and Holgeir inside the burial chambers.
 * 2) Black-Briar Lodge, outside Riften, the master bedroom.
 * 3) College of Winterhold on the shelves in the Arch-Mage's Quarters.
 * 4) Dark Brotherhood Sanctuary, look in Astrid's room for the stone. This stone can only be found while completing the “With Friends Like These…” or “Destroy the Dark Brotherhood!” quests.
 * 5) Dead Crone Rock, south-west of Markarth. The stone can be found on an altar near a Word Wall at the top.
 * 6) Fellglow Keep, can be found east-north-east of Whiterun. Look on the counters of the workroom to find this stone.
 * 7) Hob's Fall Cave. The stone is inside the Necromancer's sleeping area.
 * 8) Markarth, the Treasury House, search the master bedroom to find the stone.
 * 9) Markarth, in the Dwemer Museum. The stone will be inside, on a table behind a locked door.
 * 10) Pinewatch, a farm north-east of Falkreath. Inside the farmhouse, look for a secret entrance into an underground cave. Inside the Bandit Sanctuary, look for a locked door. Lockpick the door, inside you will find the stone on a bookshelf.
 * 11) Rannveig's Fast, north-east of Rorikstead and south-east of Morthal. Look for a prison area, and search the table with the Alchemy Lab for the stone.
 * 12) Riften, Mistveil Keep, the Jarl's Quarters.
 * 13) Solitude, just outside town, on The Dainty Sload, a boat. Look in the Captain's Quarters, on the table.
 * 14) Solitude, in Proudspire Manor. You will find the stone in the master bedroom.
 * 15) Solitude, in the Blue Palace. Look in the Jarl's quarters, on one of his shelves.
 * 16) Stony Creek Cave, can be found north of Ansilvund, south-east of Windhelm. Look in the area where you encounter the Bandit Wizard.
 * 17) Sunderstone Gorge south of Gjukar's Monument and north of Moss Mother Cavern, in Falkreath. You will find a Word Wall inside, with the added bonus of a nearby stone.
 * 18) Thalmor Embassy, look in Elenwen's Solar while completing the "Diplomatic Immunity" quest for Delphine in Riverwood. Or in the Reeking Cave on the way out.
 * 19) Whiterun, in Dragonsreach, explore the Jarl's bedroom to find a stone.
 * 20) Whiterun, Kodlak's room in Jorrvaskr.
 * 21) Whiterun, Hall of the Dead, check the wall crypts to find another stone.
 * 22) Windhelm, House of Clan Shatter-Shield, simply search the first upstairs bedroom to your left to find the stone.
 * 23) Windhelm, Palace of the Kings, look on the table in Wuunferth the Unliving's Quarters.
 * 24) Yngvild, a cave north of Winterhold and east of Dawnstar. Search behind the throne to find a bed chamber containing the stone.

Speak to Vex
Once all the stones have been recovered, return to Vex in the Ragged Flagon and she will tell that you can find the Crown of Barenziah in Tolvald's Cave.

Recover the Crown of Barenziah
Proceed to the cave and retrieve the crown that is in a part of Tolvald's Crossing, in the south-east of the caves, that specifically becomes accessible during this quest.

Beware of the trolls, and even more so of the hordes of Falmer! A Dunmer Ghost stands near the crown, but does not react to the Dragonborn.

Return to Vex
Return to Vex and she will set the stones into the crown, thereby restoring Barenziah's Crown that then ends up in the Cistern.

The Dragonborn is rewarded with an active effect called Prowler's Profit.

Keinen Zacken aus der Krone brechen