My-Hime is a 2004 26-Episode Anime by Studio Sunrise. Originally it was licensed in English by Bandai Entertainment, but after it went out of business my-Hime and its spiritual successor series and its two OVAs, My-Otome, My-Otome: Zwei and My-Otome: 0.Sifr were picked up by FUNimation entertainment and were given a new dub in 2013.
Prior to Code Geass's critical success, My-Hime was one of the most beloved Sunrise anime amongst anime fans and as a mid-2000s Sunrise Original it is considered to be one a source of nostalgia by many Sunrise Fans, and an example of Sunrise's peak in performance during the 2000s.
My-Hime's success would be followed by with a spiritual successor in My-Otome in 2005, the same year that the last episode of My-Hime aired and featured re-used character designs from My-Hime's main characters. My-Otome was also followed up by a sequel as well in My-Otome Zwei, a four episode OVA began in November of the Year that My-Otome ended and would be released across four month intervals. The Final OVA series My-Otome 0: Sifr which is a prologue to the series and features Lena Sayers who was deceased during My-Otome's plot was released in 2008. During that year it was also released that another project that would be released as well but over a decade later no new information ever came to light implying that such a project was either cancelled or that it was in fact referring to the Girl who Leapt Through Time, which shared the bulk of the people who worked on both shows, instead of a continuing part of either My-Hime or My-Otome.
Manga that were inspired by the TV shows for both My-Hime and My-Otome have been released but feature radically different plots from the anime.
HiME, or Highly-Advanced Materializing Equipment are the titular power of the My-Hime series that also refers to the girls themselves as well as the technology that came from studying them.