I recently realized that I had never read this book, and set out to rectify the omission. While dated in odd ways [the incredibly powerful computers print out results on a form of punch tape], the basic premise of the book holds up well.
One of the problems with most time travel books is that they have to weasel around the "Niven paradox," which suggests that if time travel is possible, and if you can influence your past, then eventually someone from your future will influence you, and perhaps even undo YOUR ability to travel in time.
This book was entirely about that and similar paradoxes. The basic story is about an organization of transtemporal busybodies who constantly tweak much of the history of mankind, making it "safer" and "better." A Technician in that system becomes disenchanted, after falling in love with a woman whose existence is about to be erased by an alteration, and he sets out to throw a wrench into the whole system. By the time all the twists and turns are done, nothing is what or where or when it seems. The story deals with everything from distorted social values, self-reinforcing organizational structures, and obsessive love, all in what is by today's standards a fairly short novel. One thing I really enjoy about early Asimov is the precise nature of his prose. If a story only needed 200 pages, he wouldn't write a 400-page book. Depending on the size of the print, this one is a bit over 200 pages, but encompasses the entire history of mankind in some ways.
Rather than being a nuts-and-bolts story about how to travel in time, it's a story about people, and why and whether they should travel in time.