In 2048, historians are not content to study history by reading old documents and visiting ruins. The historians in Oxford have developed a time machine and they use this machine to travel back in time and observe historic events first-hand. 

In Connie Willis's The Doomsday Book, young historian Kivrin travels to the 14th-century to view life in the Middle Ages. The Time Travel technology has built-in safeguards to prevent time paradoxes, but 2 crises strike shortly after Kivrin goes back in time:
An influenza epidemic strikes 21st-century Oxford, prompting government officials to quarantine the city and debilitating many working on the time-travel project and prompting the department head to shut down the time machine, preventing anyone from rescuing Kivrin. 
An error in the time calculations has placed Kivrin 2 decades later than they planned, leaving her in the path of the bubonic plague, just as it reaches the region of England she is exploring.

The story follows 2 parallel paths - Kivrin interacting with the locals in the 14th Century and her mentor Mr. Dunworthy trying to engineer her rescue.  Time seems to move at the same rate in both periods and both protagonists face similar challenges - a mysterious disease disrupting their society., ignorant authority figures obstructing their efforts, and the illness and deaths of those who might help them.

The book has some flaws. Kivrin's story in the 14th century is much more compelling than the 21st century story. The characters are more real and more tragic. And the science doesn't hold up as well as I would like - the 21st century protagonists have discovered the secrets of time travel but struggle to communicate because the land lines are not working properly.

But I liked it.

I liked the historical perspective of The Doomsday Book; I liked the interweaving of the characters; I liked the plausible descriptions of the physical rules of time travel (a technology that might or might not be possible); I liked the fact that the protagonist was female (rare in time travel stories); and I liked the way Willis drew parallels between the two stories taking place "simultaneously" in different centuries.

For a story with sympathetic characters, suffering a crisis of medicine and a crisis of faith, Doomsday Book holds up very well.