Many interweaving storylines, parts of a larger story of souls of the dead finding a way to "possess" living people. Fascinating overall plot, and the background future history is really interesting. Hamilton is really good at generating plausible future histories, that are incredibly well-detailed. (As other readers have pointed out, this future history is one of the few where, even though we have fusion and the ability to do wormhole-like travel between stars, space travel is very expensive, and most people can't afford it. That feels so right.) The individual plots are generally quite well-done, characters are typically interesting.
However, the sheer length of this series (which often feels like one giant novel, about 7000 pages long; it's published as 6 volumes in North America) would, I suspect, be off-putting for most readers--it definitely daunted me. Each storyline individually is not that long, but there are just so many storylines (of order 16 or so, a few new ones are introduced each volume, and a few end) that it is quite confusing; I often have to turn back to the (5-page) character listing at the front of the paperbacks to keep track, when Hamilton suddenly changes viewpoints. A little bit like Martin's Game of Thrones (ok, Song of Ice & Fire) series, except Hamilton always keeps the end in sight, thankfully.
And one grump, particular to me: so, I study neutron stars, thus, neutronium (squashed neutrons). Part of why I felt I had to read this series was, well, this book's titled the Neutronium Alchemist. In the (2-volume) Neutronium Alchemist, I read ~1000 pages before the word neutronium was even mentioned (last ~100 pages). The storyline involving it is reasonably well-done, but I have to say the book as a whole has very little neutronium in it. (I doubt any other Goodreads readers will complain about this, though.)
Ok. On to the last two volumes (another ~1500 pages!). I am quite curious how the major themes work out; he's got some very interesting future history, extraterrestrials, and theology going on. I can't recommend this series for *everyone*, but if you like hard science and space opera, don't mind some unusual theology, and read reasonably quickly and/or have ~3 months of reading time available (at my reading rate of ~80 pages/day), you might enjoy this.