I really really wanted to like this, but I just couldn't. Not my style unfortunately, but everyone keeps suggesting it so it's likely me that's the problem.
I liked how it drilled deep into themes that were important to the cultures in the story, which were very human cultures but not any specific Earth cultures. It was a glimpse into a small part of a large, coherent world.
But you have to like the characters or you can't get anywhere. People have described Stephen Baxter novels in similar ways, but I can't stand any of the characters.
That's interesting, I love Baxter's works and characters but finishing Ancillary's first book took me months and was painful. I liked the universe and the themes so I ended up reading the wikipedia summaries of the rest of the serie.
Provenance by Ann Leckie (space opera)
The Rise and Fall of D.O.D.O. by Neal Stephenson and Nicole Galland (similar themes to Anathem)