Centuries later, the head of House Lannister is Tywin, a formidable, wealthy, and ruthless lord. By Tywin's time, House Lannister has become one of the most powerful houses in Westeros, in large part due to its vast wealth. Prior to Robert's Rebellion, Tywin was Hand of the King to Aerys II Targaryen, aka the "Mad King." The increasingly paranoid king rejected Tywin's proposal of marrying his daughter Cersei to the king's heir, Rhaegar and, out of spite and paranoia, forced Tywin's son Jaime into the Kingsguard, where knights are forbidden to marry and have heirs.
When Robert Baratheon rebels against the crown, Tywin keeps House Lannister neutral until it's clear which side will win. Then, he takes his forces to King's Landing under the pretence of defending the king but actually sides with Robert. He orders the sacking of the city and the brutal murder of the royal family, and his son Jaime kills the king. Afterward, Tywin has Cersei married to Robert.
Throughout the succession crisis after Robert's death, Tywin works to grab even more power for him and his house, both on the battlefield and through strategic marriages. He consolidates his power, arranges for the Red Wedding to slaughter the Starks, and halts other alliances in their tracks. His hatred and resentment for his youngest son, Tyrion, prove to be his undoing, and Tyrion kills his father after one betrayal too many.