Source of genetic material: Yui Ikari and Lilith, the Second Angel.
Rei Ayanami (綾波レイ Ayanami Rei) is the First Child, and the pilot of Evangelion Unit 00. She is shown to be socially withdrawn and hardly interacts with anyone. Rei's cool, silent and emotionally-stunted personality has garnered the scorn of her schoolmates; Asuka calls her a "doll" or "puppet."
Although she once only associated with Gendo, she and Shinji break the ice after the battle against Ramiel, and grow progressively closer for a while. In the manga version, Rei grows a lot closer to Shinji than in the anime.
Clones of her, which lack souls, are kept hidden under the NERV building to be the supposed "cores" of the Dummy Plugs.
Also, it is hinted that Rei died twice; in the series, this stems from the fact that Rei herself says "I think I'm the third one," shortly after her death when Unit 00 self-destructed, an event that she could not remember. The first Rei is shown to have died as a small girl at the hands of Dr. Naoko Akagi for revealing carelessly (or perhaps in an intentional set-up by Gendo Ikari) to Naoko that Gendo called her a "useless old hag." The explanation is that her soul and most of her memories are transferred to one of the clones every time she dies, which then takes the preceding Rei's place as if she had not died at all.