Jaime Lannister is the first born son and thus the rightful heir to the High Lord Tywin Lannister. Jaime is a member of the Kingsguard and is known as the Kingslayer for having slain King Aerys during Robert's Rebellion. He is twins with the queen, Cersei, whom he has been having an affair with; in addition, he is Joffrey's real father.
Jaime: My point is, we don't choose whom we love. It just well... it's beyond our control. I sound like an idiot.
Myrcella: No you don't.
Jaime: What I'm trying to say. What I'm trying and failing to say...
Myrcella: I know what you're trying to say.
Jaime: No, I'm afraid you don't.
Myrcella: I do. I know about you and mother. I think a part of me always knew and I'm glad. I'm glad that you are my father.
Give my regards to the Night's Watch. I'm sure it will be thrilling. And if it's not, it's only for life.Jaime