Since I'm a writer, as well as a fan of SF and anime, I thought I'd like Texhnolyze. I really like it-- but it's NOT easy to understand it. Others have detailed the plot, so I won't try; but I will give impressions on some things that struck me right away from the first volume.
First, it's a very quiet story. No dialogue of any kind for more than ten minutes, then it's mostly one-sided (talking on the phone, to others who don't talk back, etc). Most of the setup is done in dystopic, frequently violent images, couples with disturbing sounds. For the first three episodes (out of four), this lack of spoken narrative is the standard. The slower pacing of each episode is a definite benefit, giving the viewer more time to "look around" in Texhnolyze's world.
Second, the use of clean lines and frequently washed-down colors adds to the bleak atmosphere of the episodes. The dream sequence in "Rogue 1:Stranger" is awash in white haze, with very little clear detail. (It is interesting to note that, given the plot of this series, white is the traditional color of death and mourning in Eastern cultures).
Next, the concept of a character whose clairvoyance is limited to only one of several possible futures is interesting, because psychics are not usually portrayed in such a limited way. Ran, the young girl in the (cat? fox?) mask is more realistic and sympathetic because of her power's limits.
Finally, the concept of a "Mob"-like corporation that provides its operatives with superhuman abilities for its own ends bears a certain resemblance to The X-Files, Star Trek's Section 31, and some episodes of The Outer Limits, so that will appeal to fans of general SF.
All in all, Texhnolyze has a strong beginning in this disc, but the violence and density of the plot make it unsuitable for younger viewers.