Galmar believes that he has found "The Jagged Crown's" resting place at Korvanjund. In case you didn't know, the Jagged Crown is what all the great Nordic Kings used to wear and is a sign of power to them. And so, being this great artifact of power, we have to help Galmar retrieve it.
Korvanjund is up in the mountains west of Windhelm (near Shearpoint and Nightgate Inn). Make your way to the objective to find Galmar with half a dozen Stormcloak troops, including our old buddy Ralof (who comments about you if you took the Stormcloak path in the beginning of the game). It turns out that Imperials are out in front of Korvanjund, so Galmar will give a speech and then they'll all storm the place. While I'm pretty damn sure Galmar can solo this, go along for the ride.
Note: There's a MASTER locked gate at the bottom of this place that secures some gold and a chest. Open it if you can.
Once everyone is dead, head inside. In here there are 4-5 more Imperial soldiers that the entire company will sneak up on and engage. Again, help out however you can but the Stormcloaks can handle themselves if left alone. Here Galmar will leave two soldiers behind to guard the entrance in case more Imperials come (a smart move).
Head further in with the rest of them to kill three more Imperials in a large room. Everyone will run downstairs and stop at the door there. Galmar will sense an ambush and tell them all to wait while we look for an alternate route. Take this time to loot the place (there's a LOT of burial urns here) and head up the stairs and to the floor above Galmar. You'll find a second entrance here. Use it to sneak above the ambush that was waiting. You can get down to a lower level here and attack the ambush, which results in a sort of pincer attack that you'll win as long as you stay alive.
With the Imperials dead, be sure to loot the place. You can find a few chests here as well as a skeleton holding a LIGHT ARMOR SKILLBOOK named "Jornibret's Last Dance". While you loot the team will rush ahead and kill three more Imperials before zoning into "Korvanjund Halls", so go meet them there.
In here it looks like the Imperials are having problems with the undead. Go kill them all and further in there's a corridor full of ancient wall carvings (there's also a chest past a swinging axe trap to the left). At the end of the corridor is a puzzle wall, and laying right next to it is an EBONY CLAW that holds the clue to solving it. Pick up the claw and go into your inventory to examine it (it is under miscellaneous). The claw should show the solution to the puzzle as such:
o Wolf (outer ring)
o Moth (middle ring)
o Dragon (lower wing)
Once you have them lined up like that, activate the middle lever to open the path ahead. Everyone will rush into a big room, but our progress is stopped by another iron gate. Galmar will tell everyone to spread out and search for a lever. From the gate, take a right and go through the obvious door to reach the second floor. Up here you should find an elven dagger on a pedestal. Take it. It opens up a rock door nearby. Follow the path to find a room with a giant chest. Now, before opening it, stand in the RIGHT corner near the chest, THEN open it. Take whatever's in there and you'll see why I had you stand where you did as spears come out of the floor since you opened the chest.
Head back to the big room and follow the path to another chest up above. There's also a LEVER here that you should pull. Once you do the iron door will open, but a bunch of undead will show up. Help your troops kill them and then take the next door to enter the "Korvanjund Crypt".
In here the team will rush forward to an empty room. Well, empty of all but a suspicious looking corpse sitting on a throne, and like an idiot Ralof will head over there and say "Hey guys, is THIS the crown we're looking for?". Sure enough, that corpse turns out to be a DRAUGR DEATHLORD. He'll be accompanied by two more Draugr, leading to one last big brawl (you can get in SEVERAL free and good hits knowing this info). Once it's all said and done, loot the deathlord to retrieve the crown. Galmar will task you with giving it to Ulfric while they stay and look around for anything useful.
Well, that sounds like a good idea! There's a chest behind the throne you can loot (its got an apprentice lock on it), and behind it is a DRAGON WALL that will teach you the word SAND - SLOW TIME. Very nice. Follow this path to reach a quick way to exit the temple.
Once you're back outside, feel free to fast travel to Windhelm so you can deliver the Jagged Crown to Ulfric faster. He will be pleased and asks if you ran into any trouble. Answer how you will and he will end up giving you his war axe, and telling you to go give it to the Jarl of Whiterun. It seems that it is his time to finally pick a side in this war. This ends your current quest and begins the next quest: "Message to Whiterun".