Joanna Lannister

Joanna Lannister, is an unseen character mentioned in the second season. She is deceased when the events of the series begin and is not expected to appear in the series. She is the wife of Tywin Lannister and the mother of Jaime Lannister, Cersei Lannister and Tyrion Lannister.

Background
Joanna was the wife of Tywin Lannister, the head of House Lannister and the Lord of Casterly Rock. Joanna bore him the twins Jaime and Cersei. She died giving birth to Tyrion. Joanna died when Cersei and Jaime were only four years old. Tywin took Joanna's death very hard, as did Cersei.

Season 2
Cersei has always resented Tyrion for "killing" their mother when she was a little girl, despite Tyrion pointing out that Joanna was his mother too. She says that Tyrion's "biggest joke of all" was the irony that her mother died so that a stunted dwarf like Tyrion could live. Cersei explains to Sansa Stark that she is cynical about prayer because when her mother Joanna died, she prayed for days. Because Cersei was only a four year old child at the time, she had difficulty understanding the concept of death, the finality of it, and hoped that if she prayed hard enough the gods would give her mother back. Tywin angrily took her aside and explained that prayer could not do that.

In the books
In the Song of Ice and Fire novels, Joanna was a first cousin of Tywin, the daughter of one of his father Tytos' brothers. Thus her full name was already "Joanna Lannister" before she married Tywin. She was the sister of Ser Stafford Lannister.

Though Tywin was always a stern and ruthless man, Joanna was said to bring out what little warmth he had, and he was even known to smile in her presence. Tywin and Joanna were very deeply in love, and thus Tywin took her death very hard. He became even more stern and was never known to smile again. Her death also fueled his unreasoning hatred for his younger son Tyrion, whom he blamed for killing her, combined with the shame he brought on their House for being born a dwarf.