Back on the trail, Eragon wonders what those Urgals were doing in Yazuac. Brom figures that they probably broke off from the main force to loot the place.
Brom recounts his side of the battle, then imparts a bit more info about all this magic business:
All Riders can use magic. That's what makes King Galbatorix so darn powerful. The problem is, the Riders received comprehensive training in how to direct and channel their magical powers. This means that, without his degree from Hogwarts, Eragon will be at a disadvantage in a magic duel.
Brom says that he'll do his best, though, to train him on the run. After all, Eragon has already shown promise with that whole exploding-Urgal-head trick.
To get better, Eragon will have to improve his ancient language vocabulary. Speaking the words is what releases the power. Also, it's impossible to lie when speaking in that language. Another thing to know about this language: if somebody knows your true name, they can use magic to exert tremendous power over you. For that reason, most people have two names, one they use casually and the hidden one that they keep secret. (There's no mention of how John Jacob Jingleheimer Schmidt factors in here.)
Eragon would like to know his hidden name, but Brom warns him that obtaining that knowledge can prove very dangerous.
Eragon learns that magic can also heal (though it takes a lot of energy), but Riders are forbidden to use it to raise the dead. That's something that could kill a magic-user.
Brom demonstrates some magic that's more Eragon's speed. He teaches him to cause a pebble to levitate from his palm. After a few tries, Eragon succeeds.
Brom also mentions that magic is affected by distance. The farther away from the source it is, the more energy it takes to work.
Then Brom has Eragon keep practicing with the pebble. He teaches him some new magic words, then spars with him that night after dinner. Even left-handed, Brom still has mad skills.
Their days slip into a pattern: Brom gives Eragon magic lessons during the day, sword-fighting lessons at night. Along the way, Eragon is getting stronger, as is Saphira.
After some time on the road, they come to the village of Daret.
Eragon has a nightmare about Garrow, who turns into the Ra'zac. Luckily, Saphira is there to make him feel better.