Jaime is the twin brother of Cersei Lannister and a knight of the Kingsguard, the protectors of the rulers of Westeros. He is famously known as the "Kingslayer" for murdering the last Targaryen king, whom he was sworn to defend.
Jaime is the eldest son of Tywin Lannister, twin to Cersei and brother to Tyrion. He would
be heir to Casterly Rock if he had not joined the Kingsguard, an elite order of knights whose members forswear land and marriage and owe their loyalty directly to the king.
He is notorious for betraying his solemn Kingsguard oath in the most spectacular way
possible. His assassination of the Mad King, Aerys II, earned him the name Kingslayer and widespread distrust.
Jaime continued to serve in the Kingsguard under King Robert, a situation complicated by Robert's barely-concealed contempt for the Lannisters and by Jaime's long-term treasonous (and incestuous) affair with Queen Cersei.
During the royal visit to Winterfell, young Bran Stark stumbles upon Jaime and Cersei in a compromising position. Jaime throws him out of the tower's window to protect their secret, leaving the boy permanently crippled.
Ned vs. Jaime
When Catelyn Stark takes Tyrion prisoner, suspecting him of a subsequent attack on
Bran's life, Jaime retaliates by ambushing her husband Eddard on the streets of King's Landing. He cuts down Ned's men, including Jory Cassel, before taking Ned on in single combat. Their duel is left inconclusive thanks to the intervention of one of the Lannister men, which infuriates Jaime.
Having exacted his personal revenge, Jaime joins his father in the field and takes command of a force of Lannister bannermen. His siege of Riverrun is broken by the northern army led by Robb Stark, and Jaime is captured by the Starks despite killing ten men single-handedly during the battle. Even bloodied and beaten, he remains defiant. Although he admits to Catelyn that he caused Bran's fall, he refuses to tell her his reason.
Personality and Traits
The arrogant and condescending Jaime is a formidable swordsman who relishes battle and seeks out opportunities to best his foes in single combat.
He is ruthless in defense of his family, a common Lannister trait. While his father is motivated by the preservation of their status and legacy, Jaime uses familial loyalty and affection (whether brotherly or romantic) to justify his actions - "the things I do for love".
He believes his betrayal of the Mad King was justified, although he claims not to care that the wider world has condemned him for it.
Jaime has a complicated relationship with his father, at least partly because his decision to join the Kingsguard made Tyrion the legal heir to House Lannister.