Stones of Barenziah

 are gems in The Elder Scrolls V: Skyrim. It is initially regarded as an Unusual Gem. Finding one prompts a Miscellaneous Quest to be added to the Journal, saying that the Dragonborn must appraise the gem before using it. Gems can be appraised by a few people; two of which are Maul in Riften and Vex, part of the Thieves Guild, also in Riften.

Upon getting it appraised, the Dragonborn learns that 24 exist in total and that they are only valuable as a whole set. Most are found as part of extra jobs for the Thieves Guild. The reward for collecting all of these items is the perk, Prowler’s Profit.

Locations

 * 1) Solitude, Proudspire Manor: In the master bedroom, the property must be bought by the Dragonborn first.
 * 2) Solitude, Blue Palace: On the bedside table in Jarl Elisif's quarters.
 * 3) Thalmor Embassy: In Elenwen's Solar, in a bedroom during or after the main quest Diplomatic Immunity. After completing the quest it is sometimes possible to return to the Embassy, though the area cannot always be entered by the Dragonborn. In most cases the gate and/or the door to the embassy itself will require a nonexistent key, so it is recommended to utilize one of several glitches to re-access the Thalmor Embassy if this is the case. An easy example of one of these glitches can be found here.
 * 4) Dainty Sload: On a table in the First Mate's Quarters (ship is docked between Solitude Lighthouse & Solitude).
 * 5) College of Winterhold: On a shelf in Arch-Mage's Quarters, where you can gain access during Under Saarthal quest.
 * 6) Yngvild: Chamber behind the throne in throne room.
 * 7) Hob's Fall Cave: Sleeping area (near the alchemy lab).
 * 8) Markarth, Treasury House: Next to bed in the master bedroom.
 * 9) Markarth, Understone Keep: On a table in a locked left side room of the Dwemer Museum.
 * 10) Dead Crone Rock: On a makeshift altar in front of the Word Wall at the top of the final tower.
 * 11) Whiterun: Jorrvaskr: In Kodlak's bedroom.
 * 12) Whiterun: 1st room of the Catacombs inside of the Hall of the Dead: In one of the left wall crypts near a skeleton.
 * 13) Whiterun, Dragonsreach: In the Jarl's bedroom.
 * 14) Rannveig's Fast: On a table near the watery prison.
 * 15) Fellglow Keep: On a counter in the workroom/workshop at the top of the front foyer (next to the alchemy lab).
 * 16) Windhelm: House of Clan Shatter-shield: Upstairs first bedroom on the left. Removing the Stone is considered a crime. (not any more, xbox 20/01/2012)
 * 17) Windhelm: Palace of Kings: On a table in Wuunferth the Unliving's quarters (the first door on the left of main hall, at the end, upstairs).
 * 18) Stony Creek Cave: In the Bandit Wizard's cavern.
 * 19) Ansilvund: Near Fjori's ghost in the burial chambers.
 * 20) Sunderstone Gorge: On the altar in front of the word wall.
 * 21) Dark Brotherhood Sanctuary : On the dresser in Astrid's room. *Game Spoiler-The stone can still be obtained after the Dark Brotherhood is destroyed.
 * 22) Pinewatch: In the Pinewatch Bandit Sanctuary.
 * 23) Riften, Mistveil Keep: In the Jarl's chambers.
 * 24) Black Briar Lodge: In the upstairs master bedroom.

After handing in the 24 Stones of Barenziah, the Dragonborn is asked to recover the Crown of Barenziah from Tolvald's Cave. Vex reveals that the Crown of Barenziah is an item that enhances a thief's ability. By recovering the stones, Vex can restore the paragon to its full strength.


 * There are 2 video guides available Detailed video guide or the Quick Guide

Reward
After you have completed No Stone Unturned, Vex rewards the Dragonborn with the Prowler's Profit. Afterward, the fully restored Crown of Barenziah sits on the mannequin in the Thieves Guild.

Behind the scenes

 * It is not necessary to buy Proudspire Manor. Instead, steal the Fletcher key(from they guy inside the fletcher shop, arrow shop in Solitude), then open the back door to the Manor. It isn't necessary to steal the key if you have the Wax Key perk, simply pick the lock on the Fletcher shop in solitude and the right key will automatically be added to your inventory.
 * For gems found inside dungeons where you might be fighting NPCs - they can be knocked off their table, shelf, pedestal or whatever by spells, arrows, bodies running into them, walking over them etc. and sometimes fall into inaccessible locations like a deep furrow in the ground or underneath furniture. Not sure what you're supposed to do in this case other than reload and try grabbing it before it gets knocked there.

Bugs
{[PS3]} This bug happened to us, but we went back to Solitude in the Jarls room and another stone was there (letting us complete the 24 stones).
 * Fellglow Keep: For some reason, the gem may not appear on the counter it is supposed to be on.
 * Calixto's House of Curiosities: If you have checked all 24 locations and are still missing a Stone, check Calixto's museum. Sometimes one can be found on the shelves here.
 * Entering the Dwemer Museum after having completed Hard Answers will start that quest again. To move the stone to your location without entering the museum, you can use the console command prid 7F909 followed by moveto player.
 * Alternatively, you can complete the Hard Answers quest again to score another Nightingale Blade. Subsequent Thieves Guild quests will not start again. Not tested, but this is potentially a way to obtain unlimited Nightingale Blades.
 * Before being appraised, stones will stack under the name "Unusual Gem". After appraisal they will take the name "Stone of Barenziah" and will no longer stack.
 * Have the gems appraised before finding them all. Otherwise, the quest might not be possible to complete.
 * Maul's dialogue may not show up, rendering the quest impossible to initiate.