This is the second "Xeelee" book. Again, the Xeelee play a background role.
The theme of the book is based around the concept of wormhole time travel. The idea is a variant on the Morris-Thorne wormhole [space] travel theory. That suggests it would be possible in theory to take a pair of wormhole mouths out of the quantum foam, expand the mouths and throat to allow macroscopic transverse, and then transport one of the mouths to a distant location via normal space at sublight speed. Once the mouths were in their separate places, the wormhole would provide a shortcut for travel. The variant for time travel suggests if one of the wormhole mouths was transported at relativistic speeds for a certain distance away and then back to the starting place, the time dilation effects would mean the two wormhole mouths would correspond to different points in time. Therefore, someone entering one mouth and exiting from the other would travel to another point in time. (see note at bottom)
The story tells us that Earth scientists centuries from now create such a time travel wormhole set-up. One of the wormhole mouths is sent on a 1500-year-long relativistic round trip in order to create the time difference between the two mouths. While that mouth is on its journey, the Earth comes under the domination of aliens. As the wormhole mouth re-enters the solar system, dissident humans send a spaceship to meet it and go through the wormhole. This sends those humans and their ship back in time 1500 years - to before the alien domination (and before humans had otherwise attained FTL). Those humans intend to implement a plan using their knowledge from the "future" and put it into effect in the aliens' "past", but it's not clear for some time what their plan is.
The people who've come from the future are unwilling to disclose their plan to the people in the "past". This comes to a head when the aliens send ships through the wormhole to eliminate the threat humans pose to their domination.
The final section of the book tells of one of the human characters being sent far into the future and seeing a very different state of the galaxy. What he sees did not seem to me to wrap up loose ends of the story. Rather, it seemed to raise more questions than it answers. Perhaps, that's a lead-in to later books in the series. As I haven't yet read the other books, I can't say. Personally, I found this end to the book dissatisfying. Even if that section is important for the rest of the series, I don't feel books in a series should be written to leave you with a cliff-hanger or endings that seem irrelevant to the rest of the book. (If you're publishing a single novel that's so long it's printed in more than one volume, but all the volumes are available to readers as soon as the first volume comes out - then this may not be a real issue.)
The book gives us food for thought in a number of ways. However, I found myself in a bit of a dilemma. I'm not a physicist. The wormhole time travel idea was proposed by a respected physicist. Yet, for reasons expressed in an article elsewhere in this site, I've been unable to resolve what seems to be issues. Since I've had specific [apparent] issues with this prior to reading Time-like Infinity, it raised some mental dissonance for me by reminding me of those questions. Presumably, that will not affect most readers. Most readers will find the book to be full of amazing future tech and wonders.