They walk into a two-story study that's lined with bookshelves. Ajihad is at the far end of the room, standing behind a desk. His "skin [gleams] the cover of oiled ebony. The dome of his head [is] shaved bare" (52.2).
He invites everyone to take a seat, and then another man appears. He looks identical to the jerk-faced bald guy who probed Eragon's mind. Two of these jokers?!
Ajihad explains that they're twins, but they have no names. Then Ajihad stares at them without saying anything for a very awkward stretch of time.
Finally, Ajihad turns to Murtagh. He tells him that he's not to be trusted if he won't submit to a brain probe.
Tough cookies, says Murtagh.
Ajihad says he recognizes his voice, and that it used to belong to a man "more beast than human" (52.9).
He makes Murtagh get up and take off his shirt, revealing his scar.
Ajihad recognizes Murtagh for who he is. He says that, if he won't submit to a probe, then he must be imprisoned for the duration of his stay with the Varden.
Murtagh says he'd rather die than get probed by the Uncle Fester twins, so it's off to jail he goes.
Ajihad orders everyone out of the room except for Eragon and Saphira.
When they're alone, Eragon asks about Arya, and it looks like she'll recover.
Then Ajihad wants to hear their whole story, from start to finish. Eragon obliges.
Ajihad is sad to hear of Brom's passing, but glad that he's trained Eragon to help the Varden win their war against the Empire. Then he gives them more info about the Shade.
The Shade's name is Durza. It turns out that shooting an arrow into his face can only make him mad. He's not really dead; the only way to truly kill a Shade is stab him in the heart.
Then he gives them a bit of background on the Varden's political scene:
When Saphira's egg was returned to them, both elves and humans wanted the next Rider to be one of them. Then the dwarves got in on the act, although there's never been a dwarf Rider.
To compromise, the Varden agreed to shuttle the egg back and forth from them to the elven land of Ellesméra every year, so that each would have a chance for the egg to choose its Rider from one of their own kind.
That's what Arya was doing when she was ambushed by the Shade. (The prologue is making a whole bunch more sense now, eh?).
After she disappeared, though, the elves got all miffed with the Varden. Their Queen Islanzadí broke off contact and so now the elves don't know about Eragon or Saphira.
The elves also stopped sending supplies to the Varden, so lately it's been bad times there.
Getting Arya back should smooth things over with the elves somewhat, but they'll likely demand to be in charge of Eragon's training as a Rider.
All this puts Ajihad and the Varden in a tight spot. On the one hand, they need to keep the elves happy to maintain their alliance, but on the other hand, they're guests of the dwarves in Tronjheim. The dwarves are relatively friendly to them, thanks to the order of their King Horthgar, but dwarves are no fans of dragons, who used to eat their flocks and steal their gold. Ajihad has to make everyone happy to maintain his work against the Empire.
Speaking of the Empire, Eragon has a question: Why haven't they already invaded the elven lands?
Ajihad replies that King Galbatorix is not strong enough to do that yet, but somehow his power is increasing each year.
Ajihad shows them a decoded note that was taken off the dead Urgal leader. It's burned and bloodstained, but the gist is that it contains orders for the Urgals to coordinate their forces against the Varden and attack a mystery target.
Eragon asks how the Empire knew where to find him in Carvahall. Ajihad suspects that Eragon's discovery by the Empire, along with Arya's ambush, indicates a traitor in their midst.
Dun dun dun.
Eragon wants to know what the Varden want from him.
Ajihad says that he should not ally himself with any particular faction of the Varden, but that he'll be looked to as a leader among the people. He better prepare for that responsibility.
For the short term, though, he should just rest up. Eventually, they'll need to administer a test of Eragon's sword fighting and magic skills to see where he is in his training.
What about Murtagh?
He has to stay in prison. The Varden are not big fans of his dad, and he's not to be trusted until he submits to a mind scan.
Oh, says Ajihad, I almost forgot. He gives Eragon a ring that belonged to Brom.
Then Ajihad turns to Saphira: it is an honor to meet her.
Saphira is careful. The gist—if you hurt my boy Eragon, I'll bring this volcano down around your ears.
Ajihad points out that he's got the creepy bald twins to protect him, but Saphira's not impressed. Now Ajihad turns his attention to Orik, the dwarf. He needs to be punished for disobeying his superiors, the bald twins. Eragon speaks up to defend Orik, so Ajihad reduces his punishment from death (yikes!) to being suspended. He also has to show Eragon and Saphira around the place and set them up with a room.
Eragon asks if he can see Arya, but Ajihad tells him that she'll find Eragon when she's up to a visit.