Cheris, a captain in the Kel faction, is being pulled from the front lines and brought into working with the Shuos and Nirai factions in an effort to use her intelligence to defeat the heretical faction. She would prefer to stay on the front lines with her fellow Kel, but with mathematical skills like her, others believe she is wasted there. She ends up reawakening an old "tool" to defeat the heretics that has her struggling to hold on to her sanity.
The world of Ninefox Gambit isn't the easiest to get into or visualize. The concept technology that only works because of a belief in calendrical mathematics (not a typo) is somewhat difficult to wrap my head around. Having a faction be rebellious because they believe in and use a different calendar and base their mathematics on it is actually more thought provoking than anything else in the book. The use of mathematics and algorithms to create the most effective of formations makes sense, though with how quickly Cheris comes up with them, it's clearly not a task for everyone.
Despite some initial hesitation, I did end up getting into the story, learning about the world through its characters. I actually really enjoyed Cheris' dialogues with Jedao. Some of his lessons on tactics and looking from another perspective really challenged my brain in a good way. I'll probably never be a master tactician but, as Jedao puts it, "I wasn't born a tactician. I had to learn like everyone else." It makes sense, you get good at these things through practice.
The Servitors were a delightful, regular distraction, along with Cheris' love of bad romantic comedies with ridiculously bad dueling. I really enjoyed Cheris' interactions with the Servitors and their own appreciation of her treating them as allies instead of mindless drones.
Overall, I really did enjoy this book. It has a lot of death, and I do mean a lot. Joining the Kel is considered to be a suicidal move and there are many battles and heart-wrenching situations. For all it's death, though, there are moments so full of humanity that it carries you through the entire book. If you're okay with reading about major wars and have any interest in using mathematics as the basis of a culture, I highly recommend this book. Not for everyone, but still a nice mental workout.