Casterly Rock

Casterly Rock is the ancestral stronghold of House Lannister, and the regional capital of the Westerlands. It is located on the Western coast of Westeros on a rocky promontory overlooking the Sunset Sea. It overlooks the major city of Lannisport.

A major goldmine is located under Casterly Rock. It is one of the most productive in the realm and provides House Lannister with their wealth.

Background
According to legend, Casterly Rock was found and held by House Casterly after its founder slew a pair of fearsome lions that lived in the gold-filled subterranean cave where the castle would be built upon. They were hoodwinked into giving the Rock to Lann the Clever, a legendary trickster and ancestor of House Lannister, thousands of years ago, during the Age of Heroes.

Season 1
In the Red Keep, Lord Eddard learns that Ser Gregor Clegane has been scouring the Riverlands. Aware that Clegane only follows Tywin Lannister's orders, he pronounces Clegane a criminal and instructs Grand Maester Pycelle to send a raven to Casterly Rock and inform Lord Tywin Lannister that he must come to King's Landing and answer for Clegane's crimes —if he doesn't depart Casterly Rock and arrive at King's Landing within the fortnight, he will be branded a traitor and enemy of the Crown.

After the arrest of Lord Eddard Stark following his failed coup, Theon Greyjoy suggests to Robb Stark that they should march on Casterly Rock in retaliation. However, Robb refuses.

When Jaime Lannister is taken prisoner by Robb Stark in the Battle of the Whispering Wood, the Lannister bannermen hold a strategy meeting and Leo Lefford suggests they can't march on the Starks at once —they must first return to Casterly Rock and raise levies.

Season 2
Theon Greyjoy tries to convince his father Balon that, if they pledge fealty to Robb Stark and fight for the Starks in the war, the Greyjoys will be given Casterly Rock as a reward once the war is over. Balon refuses, as he claims the Greyjoys are not subject to anyone and take what is theirs.

In Harrenhal, Tywin's bannermen discuss whether to march against King Robb or King Stannis, and Tywin notes that Robb is too close to Casterly Rock, but his brother Lord Kevan argues that, since the Greyjoy's attack on Winterfell has divided Stark's forces, Robb won't risk marching on Casterly Rock until he is at full force. In King's Landing, acting Hand of the King Tyrion tells Varys, the Master of Whispers, that he never expected to have any real power — While his brother became the youngest Kingsguard in history and his sister became queen at nineteen, Tyrion was merely put in charge of the drains and cisterns of Casterly Rock.