For my money, this is the best of Baxter's highly variable output. My main grouch is that the title is wrong. This is the book in the manifold series that should be called 'Time'! Baxter conveys a wonderful impression of the depth and strangeness of the future. By contrast, although there is plenty of star hoping, the book's main action centres on the solar system itself.
The chief challenge in any novel spanning centuries and millennia is to maintain a continuity of story. How do you sustaina point of view or the audience's connection with character? We could probably have a long debate on the different techniques used in science fiction: longevity, family trees, hibernation, even reincarnation (thanks to Kim Stanley Robinson), etc.
In Space, Baxter relies partly on longevity and a form of hibernation (characters go off-line while traveling between the stars) but he never really solves the problem. The story is episodic, like a collection of connected short stories.
Nonetheless, Baxter is endlessly inventive - an idea a page and many are highly original: a nuclear reactor manned by neanderthals, vacuum flowers, tunnels to the centre of the moon, trees in orbit, seas on triton, a galactic ecology ...
Space is also a thorough working through of the Fermi paradox. If life is abundant (which we would expect) where are they? The answer is a depressing and endless cycle of expansion, exploitation, collapse and sterilization. Sometimes this point is hammered home too hard and too frequently. But equally, and subtly, Baxter draws parallels between the earth-bound and intersteller histories. You're never lost in a stark, sterile 'future history' (a la Stapledon) but very much mired in the muck and blood of human life.
Space is eerie, evocative, thought provoking and, ultimately, depressing. Like so much of Baxter's work, it is a challenge to our sense of place in the universe. As such it can be a painful read, but it sticks with you.