Yui is the mother of Shinji Ikari and the wife of Gendo Ikari, was a brilliant bioengineer who worked for Project E at Gehirn. Additionally, she is the daughter of a prominent member of Seele.

Yui Ikari is one of the more powerful presences in the series, Yui is shown to be kind, optimistic, and motherly. Her faith in humanity and belief that it is worth preserving and remembering stand out when compared to the more cynical characters on the rest of the cast.

Yui became romantically involved with a mysterious man, several years older than herself, named Gendo Rokubungi, who was constantly the source of shady rumors among them that Gendo had approached Yui for nothing but her talent and her affiliation with Seele. Regardless, in Yui's own words, he was "quite a sweet person. It's just that no one knows it."
In the rebuild film series she's reffered to as Ayanami Yui instead of Ikari Yui




After Yui (presumably) graduated, she married Gendo, and the latter took on her surname He became involved with Seele, joining the Katsuragi Expedition to serve as an auditor, although it is not revealed what Yui was doing during this time. After Gendo returned, they had a child together, Shinji who, if a girl, would have been named Rei.


(Source: Evageeks)