Take Up Arms (quest)

Train with Vilkas
After finishing Speak with the leader of the Companions in Jorrvaskr, Kodlak Whitemane will charge you with your first quest in the order of the Companions: you must engage in some hand-to-hand combat with Vilkas to test your mettle.

Follow Vilkas outside. The battle is simple enough: just swipe your weapon(s) at him a few times and it will be over. He will just hold up his shield the whole time.

You will not be able to use magic against Vilkas, unless you use bound weapons, see this video example.

Take Vilkas' sword to Eorlund
After the skirmish, Vilkas will charge you with his sword, Vilkas's Sword, to be taken to Eorlund Gray-Mane, a close ally of the Companions at the Skyforge in Whiterun.

Speak with Eorlund and give him the sword. You can discuss some of the Order's history and Eorlund's personal role in it.

Bring Alea her shield
Eorlund then asks the Dragonborn to bring Aela's Shield to the huntress. Aela will likely be waiting in her room in the Jorrvaskr Living Quarters.

Here, you can talk history again and learn more about the Companions, or you can cut to the chase and hand over her shield from Eorlund. After you lose the shield, she and Skjor will discuss your recent test with Vilkas. If you want to play nice with Aela, choose "I don't care for boasting" when the option comes up in the dialogue. Aela likes men of action, not of words.

Follow Farkas to your quarters
Aela will then call in Farkas who will point out the Dragonborn's quarters in the basement.

Bugs

 * Take care not to use magic on Vilkas when he is testing you. There are reports if a glitch where Vilkas will not stop warning you not to use magic and not being able to use any stores or NPCs after.
 * When accompanied by a follower the initial attack by Vilkas will make the follower defend the Dragonborn. And even after Vilkas is "defeated" the follower will not stop attacking. Solution: park the follower out of sight before engaging with Vilkas.

Zu den Waffen (Aufgabe)