Okay, now I'm intrigued.
Xenakis. I know the name, am aware of his importance, but have heard very little of his music. And of that "very little" -- that snippet of Herma on Youtube -- it appears to be very disjunct, atonal and pretty damned cerebral. I know there must be more. Takahasi is an incredible pianist, by the way. Gawd, effortless technique grappling with galloping thickets of notes. 
Could those of you who admire him, tell me what his compositional aims are? Is his music in opposition to other modernist compositional schools, or a movement towards something totally new. It strikes me, very superficially, as very complex, athletic atonalism, at least for the keyboard. I can't imagine the enormous technical and intellectual resources needed to play his music. It doesn't appear to be accessible on a first, superficial hearing, either.
What structural forms does he favor? Is he consistently atonal or does he use serial techniques that float around key centers?
What should I be listening for? What makes Xenakis so special? Why should I get to know him better? He sounds like a lot of work, so I would appreciate some good reasons from people who know his music, as to why I should bother.
Thanks in advance to anyone who wants to enlighten me here.
Xenakis is a stochastic composer, which means his works are written based upon mathematical principles. Herma is written using boolean algebra; I will take a picture of the graph (it's in his book Formalized Music) tonight when I get home and show you. His works are based on many different formulai such as but not limited to Markov Chains, Game Theory, Group Theory, Boolean Algebra, Banach Spaces and Vector Calculus (many composers would then go on to write music based on vectoral mathematics, which is now called "Spectral" or "Post-Spectral" music), and a lot of it is not WRITTEN by computers, but he did often plug his formulai into computers. He is also one of the pioneers of electronic music, some of his major electronic works being Diamorphoses, Kraanerg, La Legend d'Er and Persepolis. His music was, at the time, very much in opposition of some of the modern schools, as he felt they limited artistic freedom, although I personally find that to be somewhat in contradiction with using a computer and some Calculus to write a piece, but what do I know XP In a good deal of his earlier major works such as Metastasis, Pithoprakta, Acchoripsis and Duel, he would try to distinguish the sounds he created by certain variables, which were rate, density, volume and sound (like glissando, pizzicato etc). The works are not meant specifically to be "complex" or "athletic", although the form he wrote in gave absolutely no baring to the limitations of the performer so many of them are some of the most difficult works in existence, such as his piano concerto "Synaphai", which is arguably the single most difficult piano piece, with the possible exceptions of Finnissy's "Folklore" and Barrett's "Tract". His string quartet, ST/4, is also possibly the most difficult string quartet also, with the only possible exception being Ferneyhough's.
Anyway, as he is my favorite composer, I have sheets and recordings to pretty much everything Xenakis published (and even two unpublished pieces), and I could probably share them with you if you wanted to study him further

Also, there is a video of Synaphai on youtube, along with videos and recordings of several other pieces of his. I would recommend finding recordings of Metastasis, Evryali, Kyania, La Legend d'Er and Palimpsest before getting into some of his more complex works.