Although it takes place centuries after
The Fall of Hyperion,
Endymion seems to pick up right after the end of the last book. This is the third book in Dan Simmons's "Hyperion Cantos." Since it's the first book of a second duology, you could start reading with this book, since the entire universe is pretty much introduced anew, but there are so many references to events that took place in the first two books, now history in this one, that you will probably feel like you're missing a lot.
At the end of
The Fall of Hyperion, the Hegemony of Man was falling, due to the attack of the Ousters who weren't really Ousters but constructs of the TechnoCore. As
Endymion begins, the Hegemony is history, and now human space is ruled by the Pax; a resurgent Holy Roman Catholic Church empowered by the cruciform parasites we encountered in
Hyperion, which allow anyone to recover from any injury and be resurrected from nearly any fatality. The Pax has figured out how to control them so that people who receive the cruciform are not turned into mindless idiots, which means that the Church now
literally offers eternal life.
The child of Brawne Lamia and the cybrid Johnny Keats emerges from the Time Tombs, and the Pax views her as a threat to all of mankind, for reasons that are not clear until the end. So they send starship captain Father-Captain de Soya to "fetch" her. Meanwhile, that irascible dirty old man Martin Silenus is still kicking around, and he recruits Raul Endymion, a native of the planet Hyperion who fell into a little trouble with the Pax, to go save her. As he tells Raul, he doesn't just want Raul to save his god-daughter from the Pax. He also wants Raul to destroy the Pax, find out what the superhuman artificial intelligences known as the TechnoCore have been up to these past few centuries, oh, and take down that enigmatic, unstoppable alien killing machine known as the Shrike. No problem.
Endymion alternates between the POV of Raul Endymion and Father-Captain de Soya, adversaries but both of them ultimately good guys if not always serving good ends. There's plenty of interplanetary space opera drama and action, but for me it didn't really get good until the final few chapters when conspiracies begin to be unveiled, and of course, we finally got the kick-ass battle with the Shrike we've been waiting for.
Like
Hyperion,
Endymion ends very much on a "To be continued" note. Either of the two duologies can be read independently, but definitely read the first book of each first (and if you like it you will certainly have to read the second).
I recommend reading the first two books first because frankly, they are better.
Endymion isn't bad, but it's a solid 3.5 stars - great epic space opera if you like epic space operas, but whereas Simmons dropped a whole lot of finely-crafted worldbuilding with star-spanning conspiracies and multiple existential alien threats in
Hyperion and
The Fall of Hyperion, in this third book, there's not so much new as building on what he introduced before. If you are a dedicated consumer of space opera, this is above average for the genre, but falls short of greatness, and really I think the series could have ended with
Fall of Hyperion. But I will go on to read the fourth and final volume.