1633 by David Weber and Eric Flint
I admit, as much as I enjoyed 1632, I picked up this book with trepidation, because I've heard rumors of Weber's penchant for excessive description of how weapons etc work. But I was in the dealers room at LibertyCon while Flint was signing things, so I bought the book to get signed.
This picks up 6 months or so after the end of 1632. Mike Stearns is president of the US, Gustav II Adolfus is rebuilding Magdeburg, Rebecca Stearns has led a diplomatic mission to Holland to try to convince them that Richelieu is a lying double crosser, and Rita Stearns Simpson is in London trying to convince King Charles (or his advisors) that Richelieu is a lying double-crosser.
The history books from the Grantville High School library have made their way around Europe. Charles kills Oliver Cromwell's family and throws him in the Tower of London, where the Grantville delegation is staying (in the nice part). Richelieu uses them to his advantage, too, convincing Charles to sell/swap him the entirety of their colonies in the New World.
There are a lot of plot threads woven together here, far too many to discuss in any detail. It becomes obvious why 1634 has 4 books, and 1635 4 as well (or something like that).
There were mercifully few passages wherein the details of how something works were discussed in minuscule detail. There are people who enjoy that sort of thing, and I can appreciate the effort it takes to figure out how to build an airplane with technology and materials available in the 1630s plus whatever got zapped along with Grantville, but my eyes glaze over while I'm reading about how cannons are being made and whether they're smooth bore or rifled, breech- or muzzle-loaders and why. I skim those sections and hope it isn't important later.
There's still a bit of "America! Fuck yeah!" jingoism, but less than in the first book, probably because there's so much shit hitting the fan.
Some people might find the idea of spreading democracy problematic, in light of current American foreign policy. I can agree and disagree there. By the end of this book, the Americans are stepping rather sideways from the leadership position and letting the Germans (and Swedes) start their own party. The radical change from 17th century monarchy to 21st century American democracy will come at its own pace. Also, in the mid-17th century, anti-monarchist sentiments were already extant, so the peasantry and non-nobility now have a model that works (to some extent).
Fans of well-researched alternate histories with political intrigue and grand battle scenes should enjoy this series.