They head off, Eragon riding Snowfire and Murtagh on his own horse Tornac.
They sell Eragon's old horse, Cadoc, at a small village and continue on.
During their journey, Eragon learns more about Murtagh: the Empire is chasing him, but he won't say why. Also, Murtagh seems to know a lot about the political workings of the Empire.
They head north, past the capital city of Urû'baen, and keep on rolling. Along the way, Eragon has his sixteenth birthday. They stop off at a Chuck. E Cheese and play ski ball all day. Just kidding. In the middle of the wilderness, Eragon doesn't even bring it up. Sad.
Saphira is getting bigger, too.
Eventually, Eragon is well enough to spar again. He takes on Murtagh, but they are equally matched. Both are super-duper swordsmen, so they push each other to hone their skills.
Eragon also practices his magic, and shares what he knows with Murtagh.
Finally, they reach Gil'ead, "a rough, barbaric place filled with log houses and yapping dogs" (39.30).
Murtagh convinces them that he should go into town by himself to track down this Dormnad, seeing as how, you know, Eragon is the most wanted man in the kingdom and all.
Murtagh takes off, then comes galloping back a long while later. He's set up a meeting with Dormnad at sunrise the next day.
Unfortunately, Murtagh was recognized in Gil'ead by someone who knew his face. They don't think that will mess up the meeting, though. Sure it won't, guys.
The next morning, Eragon's scar tingles ominously. Saphira smells horses nearby and an unfamiliar stench.
All of a sudden, an Urgal appears at the edge of their camp. Eragon blasts him with some magic, though.
Wait! It was a diversion. The rest of the Urgals storm the campsite. Eragon kills a few, but then he's bonked on the noggin by a club.
Eragon slips into unconsciousness. (This whole passing out at the end of a chapter thing is getting out of control.)