Forbidden Legend

Background
"Long ago, the Archmage Gauldur was murdered by his three sons, who stole his amulet of power and divided it among themselves."

Once the three sons divided the amulet among themselves they began a rampage around Skyrim. This attracted the attention of the High King of Skyrim, so the King sent a group of battlemages to kill the three sons.

Quest

 * "In Geirmund's Hall/Folgunthur/Saarthal, I found a cryptic message on the body of a powerful Draugr, condemning him for his ancient crimes. What was his story? Why was he entombed with a broken amulet?"

Or "Long ago, the Archmage Gaulder was murdered, and his three sons were hunted down by King Horald's personal battlemage. The entire incident was covered up, their names struck from every record. But the legend survived. Perhaps someone still knows the truth of this ancient tale."

Quest Progression
Objectives: Investigate the Gauldur legend.

Walkthrough
There are multiple ways to begin this quest. First is by reading the book "Lost Legends" found throughout Skyrim. Please see Lost Legends locations for more information on their locations.

The quest can also be activated by reading a Writ of Sealing in any of the burial locations, or by taking a Gauldur Amulet Fragment from the bodies.

Saarthal Excavation
In order to gain access to the excavation site, you must first begin the quest Under Saarthal. This quest is found in The College of Winterhold, but don't be discouraged if your character is not skilled in magic. You can easily enter the Сollege after completing the very short quest First Lesson, regardless of magic skill, and then start Under Saarthal by speaking with Tolfdir after his magic demonstration. Defeat Jyrik in Saarthal, by the orb, and take his Writ of Sealing and his Gauldur Amulet Fragment. Read the writ to start the next quest point. Then, go to the Arcaneum and read the book Lost Legends (on a small table on the right hand side of the room, behind the pillars not in the middle, as you enter) to get the next clue about the origin of the Gauldur Amulet Fragment.

Folgunthur
Travel to Folgunthur and read the journal of Daynas Valen in the camp outside the cave. It will tell you about his travels with the Ivory Dragon Claw. He traveled to Folgunthur looking for the Amulet. Follow him inside, past the corpse of his compatriots. He will be lying on a Claw button next to a bridge. Take the Claw and his notes, read them, and activate the button to cross the bridge. Eventually you will come to a room with two thrones, facing a chain lever, and a grille in the floor covering a staircase. To enter the rooms you must pull a lever which opens one room and closes the door on another there are a several Draugr to kill, in one of the rooms you must get the turning stones to match and then pull the chain lever. Manipulate the pillars to match the symbols in the adjacent room, then pull a chain to open the grille. Descend and deal with two Frostbite Spiders in the room below. You will soon come to rotating-ring puzzle, similar to Bleak Falls Barrow. Dispatch several Draugr, then have to use the Claw's closeup to determine the answer to the puzzle. Once inside, fight Mikrul Gauldurson, and take his Gauldur Amulet Fragment and enchanted sword, Gauldur Blackblade. After beating him, use the claw to gain access to the two rooms on the back wall. One has a shout, that can complete a miscellaneous quest, and then proceed to leave by using exits blocked from the other side.

Geirmund's Hall
Geirmund's Hall is a dungeon close to Ivarstead, grave of the hero Geirmund. Travel there and upon entering the cave, you will come to a hole in the ground, drop through it. There is an underwater alcove, with a chest and a Potion of Waterbreathing. Climb up the steps and enter a room with a puzzle, the order of the stones starting from the first one is Eagle, Whale, Snake, Whale. Activate the lever by the door. The next room, after fighting a few Draugrs along the way you come to a large room and after climbing the steps, immediately to your right is an altar with the body of Geirmund holding a key. Take the door behind you, and follow the path to the left, you find a Drauger Deathlord after you kill him you reach a dead end and a lever on the ground; don't pull that lever as it's a trap but if you look directly opposite it you will find another lever; pull that one instead and the drawbridge will drop.

Then face Sigdis Gauldurson, the hardest of the three sons. There are four sigils on the ground in the cave where you fight him. He will teleport to whichever three you are farthest away from and make two copies of himself. All three will attack you, including using Shouts like Unrelenting Force and, at higher levels, Disarm. If you attack one of the clones, it will dissipate after one hit, and after both clones have died Sigdis will teleport away again. It is possible to tell Sigdis apart from his clones because he is the only one with the true health amount (the clones will have full health), and also by the fact that his clones, being summoned, will be surrounded by a bluish glow, in addition the "real" Sigdis can be identified by being the only one wearing an Ancient Nord Helmet, with his helm's decorative horns curling downwards; the horns on his clones' helmets will be curled upward. After you have killed him, take the Gauldur Amulet Fragment.

Gauldur's Grave
Door Combinations:
 * 1) Emerald Claw: Bear, Dolphin/Whale, Snake
 * 2) Ivory Claw: Hawk, Hawk, Dragon

After all of the fragments have been collected, go to Reachwater Rock, near Karthspire. Inside, you will find a dead Adventurer near the Emerald Dragon Claw, on a pedestal along with a note warning would-be explorers away from the site. Enter the claw door using the combination inscribed on the palm of the Emerald Claw, Bear, Whale/Fish, Snake. Inside will be yet another Claw door, this time using the Ivory Dragon Claw's combination. Before placing the three amulet fragments on the pedestal, cast a Fire Rune at the foot of each Sarcophagus. This explodes killing each Draugur inside making fighting the Ghosts easier. Place the three amulet fragments on the pedestal to make the ghosts of each son to appear which you will have to fight in turn.

Sigdis will use the same tactics as before, disappearing and reappearing to shoot arrows at you, using four out of the six possible locations. Take advantage of his teleports to abuse the wait function, restoring your health and providing a handy autosave. The real Sigdis has a slightly different helmet model (iron helmet) than his clones, and his clones will always have full health, and be surrounded by a slightly bluish glow.

After Sigdis, Jyrik will appear and summon a Frost Atronach to help him, occasionally teleporting around the room.

Once all three sons have been defeated, they will reappear as ghosts above the pedestal, then vanish. Archmage Gauldur will appear and reforge the Gauldur Amulet Fragments into The Gauldur Amulet, a necklace that grants +30 to health, magicka, and stamina.

Don't forget to loot Gauldur's skeleton before you leave, as it holds a decent amount of money.

Bugs

 * Reading the note before you got the quest will make you unable to progress further, subsequently reading the Writ does nothing. The only known way to fix the quest (if you got it by killing Jyrik) is to obtain a copy of "Lost Legends" and read it. Then the quest will progress correctly.
 * During explorations, if you locate Daynas Valen and go inside, he will be immediately hostile to the player even if you have not yet begun this quest. Once the quest has begun, despite killing him at his house, Daynas's body will be in the ruin where you can get his journal and the claw.
 * In the attempt to access the shout within the Folgunthur Crypt, after killing Mikrul Gauldurson and the other Draugr thralls, the march music may just proceed without a shout being given to the player. Reloading does not fix this bug.
 * Occasionally the pillar puzzle in Giermund's Hall will not work. No known method of fixing this. Reload recommended.
 * If you enter and clear Geirmund's Hall before starting the quest, Sigdis' body and amulet fragment will disappear; a marker will hover where the body was when you defeated him.The trick is that you must do this at the location that you kill the boss. At the console:
 * prid a5e68
 * enable
 * Exit console mode and loot the body for the fragment. the journal will be updated, and you can complete the quest normally.
 * on the 360: A fix for the disappearing sigdis amulet is this: complete the other steps as normal, and when you return to Giermund Hall, the quest arrow will be pointing to the now present body of Sigdis. Not sure if it always works.
 * If you enter the lair with Mikrul Gauldurson already out of his tomb, there is a chance you can't loot his corpse after killing him. You may want to reload your last save, go back to his room, and if he is out of his tomb again, simply back out of the zone and re-enter. He should be in his tomb, where you can quickly kill him, and loot him after.
 * Sometimes Mikrul Gauldurson will be impossible to loot even when he comes out of his tomb. Try killing him without sneaking, with a different weapon, such as a sword instead of a bow, or killing him last after killing the other Draugr. This should make him lootable.
 * If the amulet in Saarthal is not picked up before the Eye of Magnus is moved there is a chance it will disappear along with the corpse of Jyrik.
 * At a high enough level Sigdis can use the "Disarm" shout to remove your equipped weapon, if you are standing in certain parts of the dungeon the weapon may be dropped outside the mapping making it impossible to retrieve.
 * Disintegrating any of the three bosses will prevent the triggering of the script which forges the amulet, trapping you in the room.
 * Killing the thralls while in the sarcophogi prevents them from spawning during the battle.
 * Killing or paralyzing Sigdis before he teleports for the first time, such as with a fatal sneak attack, the Paralyze spell or enchantment, or the Unrelenting Force shout, can cause him to fail to reappear or reappear paralyzed and unattackable, making it impossible to retrieve his Fragment.
 * Sigdis' Unrelenting Force attacks can push the player up onto the platform where Gauldur's body sits. Once up there, the player will not be able to come down again (they'll be stuck behind an invisible wall), and Sigdis will not be able to attack the player. You escape using the 'tcl' console command, or by reloading a previous save.
 * Sigdis' Unrelenting Force can push a player through the gate on the opposite side of the amulet pieces causing the player to be stuck there until the amulet is reforged
 * In case there are any problems in completing the quest, here is a list of the relevant items, for use with 'player.additem'.
 * Lost Legends: 000ED608
 * Sigdis's Gauldur Amulet Fragment: 0002D753
 * Mikrul's Gauldur Amulet Fragment: 000F1C17 (on French version: 0002D74F)
 * setstage dunGauldursonQST stage 31/32/33
 * Other bugs can probably be solved by reloading your last save or autosave. Good luck and save often!
 * If you have an NPC who is following you for a specific quest, they may become hostile to the ghost of Gauldur, preventing the finish of the quest. You can just attack them until they submit and it continues as normal.
 * If you are quick enough after killing the ghosts you can loot their bodies for their weapons again.
 * Killing Sigdis just before he is teleporting might make him disappear. Reentering Geirmund's hall solves this.
 * In the Reachwater Rock section (where you go to combine the amulet fragments), it's possible to get stuck on the platform where the defeated spirits are standing. This could prevent finishing the fight and/or collecting the completed amulet (and leaving the cave). Try to avoid jumping up there; otherwise you'll need to reload a previous save.
 * During the final battle, disintegrating any of the 3 brothers with a lightning spell will cause the ash pile to reappear on the altar but the quest will not advance, Tried with disintegrating 1, 2 and all 3. The only way to fix this is to reload a save before the disintegration.
 * If you received the quest before going to the College of Winterhold, you will not be able to enter Saarthal or pick up the amulet inside until you listen to Tolfdir at the college. (Where he teaches you to use a ward spell.)

Trivia

 * The battle with Sigdis and the way he fights is strikingly similar to the Wizzrobes of the Legend of Zelda series. Both enemies teleport around the room to designated spots, make clones of themselves (which can be picked out from the real one with a sharp eye) and shoot projectiles at the player.