The premise is simple: What if you changed Harry, but all the other characters remained the same? The big change is that here Harry is an intelligent rational scientist (there are some other, but more minor, changes). And that makes all the difference: Harry the rationalist, confronted with magic!
It starts out a little weak, as Yudkowsky gets to grips with the writing process. It gets funny, as Harry gets to grips with the fact that magic exists, and that it works. It gets interesting when Harry’s rationality gets him sorted into Ravenclaw, and as he decides to bring Draco Malfoy under rationality’s wing. It gets clever when the Professor for Defence Against the Dark Arts starts teaching the students how to fight with magic. It gets dark when an appalled Harry discovers Azkabhan. And it gets devastating when [well, that’s enough spoilers for now].
When I finished reading online, I downloaded the pdf version. All 2007 pages of it. (Neal Stephenson, eat your heart out!) That much material, dense with foreshadowings, references, and allusions, read over several months, meant there were things I forgot, and things I didn’t spot. No matter, there's a whole TVTropes sub-site, to suck up another significant portion of my life.
The main story is only (only!) 1969 pages. There are also a few pages of mostly hilarious omake (extras), including some cut scenes and alternative scenes, and some scenes from alternative fictional worlds the rational approach is applies to (including Lord of The Rings, Narnia, Anita Blake (ahem), Twilight, Moby Dick, Alice, and, of course, Hamlet).
The key point, beyond being rational, is the characters Harry and Voldemort have very similar responses to the concept of death, but with one critical distinction (who’s death) which leads to their very different actions. I discovered after I started reading that Yudkowsky is a transhumanist, which certainly explains some of the underlying themes; it crucially makes for a reason for everyone to care about the Philosopher’s Stone.
As well as all the rationality, and plot divergences, there is general poking fun at some of the sillier bits of the original, particularly the scoring system in Quidditch. Overall, this is a fantastic read, particularly if you are a nerd with pretensions of rationalism. I really enjoyed it.