By Connie Willis.
I should probably say up front that I liked Eifelheim better. More about that in a bit.
This book is about a determined young student who manages to convince... someone... that she should be allowed to travel to the 14th century. Of course, you know from the beginning that it can only go downhill from there...
What I liked: As a disaster story, it's not much good if you don't care about the characters. The problem is that I didn't care much about the modern characters, only the medieval ones (and Kivrin and maybe Mr. Dunworthy). Despite all the things I didn't like, it's quite readable. You get history as part of the deal.
What I didn't like: It's a disaster story, and it's depressing. The end isn't any kind of triumph, just survival. Too many characters are introduced too quickly which makes it a little hard to keep track of who's who and who's important. The Middle English dialogue is just short of impenetrable but fortunately you get to read it in translation after a little while. The theology is heretical or worse (Dunworthy thinks that God wouldn't have sent his son if he had known what would happen, and that he didn't stop it because he couldn't). On the trivial side, the phones seem very dated next to a future that has time travel and (kind of) advanced medicine.
It's inevitable that Eifelheim is compared to this book. They both involve parallel stories between the present (or future) and the Middle Ages. There is also a priest in both who turns out to be a good guy (the one in Doomsday Book isn't nearly as intellectual but he has a servant's heart). Eifelheim, though, seems to go somewhere with the story, while the characters in Doomsday Book end up almost where they started, perhaps slightly wiser, but really just alive. (Except for the ones who die.)