When this book came out, I faced a bit of a conundrum: a time travel book (which I hate) by Kim Stanley Robinson (one of my favorite authors).
Which was it? Kind of both. Overall, the work's an only-moderately-coherent mess. There are aliens! Time travel! Inquisition!
Basically, the book follows Galileo from his invention of the telescope to his death. From that point on, he is watched over by a guy from the future, and is occasionally grabbed 1500 years ahead to be a pawn in an internecine struggle among people living in Jupiter's Galilean moons at the beginning of the fourth millennium.
This is going to sound more complimentary than I mean it, but in some ways the book reminded me of War and Peace. Not just because it perhaps overstayed its welcome, but also that a major portion of the book (the trips into the future) seemed an excuse to juxtapose Galileo and later scientific thought. Which is not without its interest, but I don't think can carry the book.
One thing I found interesting is that the author subtly set the future bits in the world of the Mars books, with references to the Accelerando and Bao, the physicist from those books.
The historical Galileo segments were actually quite interesting, and I think a more focused historical novel about Galileo might have been a more interesting choice. Particularly because I felt the narrative escapes to the future let the reader off the hook a little, especially when things get bad for Galileo.
Like the areology in the Mars books, there's clearly a fair amount of scientific material here that I missed the first time though this book. Unlike the earlier series, though, I have no interest in going back to try to improve my comprehension of it.