Old Dragon Riders
Galbotorix won the battles over who was going to be king. He killed every rider who had a chance to kill him. He tried to kill Eragon but had failed every attempt.
Brom survived the battles because of his dragon that tried to protect him but got killed by Mozan. Brom hunted him down after the king won him over. He took his sword and drove it through his heart and now wishes he didn't because they had a chance to kill Galbotorix.
Galbotorix became king after he won all the battles. He has two dragons in the book Eldest. He also got Eragon's brother by kidnapping him and forcing him to join him or he would kill him. Eragon's brother got one of the 2 remaining eggs to hatch.