Shin Tenchi Muyo (with Shin written with the Kanji character for 'true' instead of 'new') was also the title of a series of Tenchi Muyo! novels in Japanese, written by Yosuke KURODA and Masaki KAJISHIMA(one of the original creators of Tenchi, and also responsible for the anime Dual! and Agga Rutter).
The three novels in the series, "Jurai", "Yosho", and "Washu", are essentially prequels to the Tenchi OVAs. The novels tell about Washu's past at the Academy before her kidnapping, the events that led to Ryoko's attack on Jurai, and Aeka's first duel with the space pirate. Other revelations include Yosho's first crush(not Aeka - her mother, Misaki) and his first girlfriend (a Galaxy Academy student named Airi), Lady Funaho's problems adjusting to Jurai - and how Misaki's friendship helped her, and how Aeka and Sasami's grandmother, Seto, all but forced the Juraian emperor, Azusa, into the royal family.
These novels have become more important to Tenchi Muyo! fans recently; the latest Tenchi TV series to air, Tenchi Muyo! GXP, is based on both the OVA continuity and the Shin/True Tenchi novels; several of the new background characters from them appear, and Airi and Seto are major members of the supporting cast.
This information obtained from the site Tenchi Muyo in the World, which contains partial synopses of the Shin/True Tenchi novels in english.
There is no complete English translation of the novels available, as far as I know.