Blind Descent is a pretty good book that covers the Krubera expedition as well as the Cheve cave in Mexico.
Current estimates of caves for the United States are around 50-100k. I think you will want to refine your scope.
If you are looking for a good book to buy someone who is interested in caving, consider one of the following:
NSS Cave Minerals of the World.
Blind Descent.
The Longest Cave.
Anyone interested in cave-diving and the obsessives who can stomach squeezing through the tiniest of holes just to see what may or may not be on the other side, may want to check out "Blind Descent" by James Tabor:
https://www.amazon.com/Blind-Descent-Quest-Discover-Deepest/dp/0812979494
It's one of the few non-fiction books I've ever read that really gets my pulse racing. Imagine, for instance that after a couple of weeks into the descent you finally get to the point where the previous expedition had to turn back. You're already hundreds of meters into a "new" passageway, a channel bending it's way through the immovable rock, so narrow you are now scooting forward on your butt and it's difficult just to point your flashlight ahead of you because you can't get your head up very high and your feet are in the way. Then you come to a point where the passage narrows down. Most of us would turn back. These people try to squeeze through. Some of these narrows are so tiny you have to breathe out completely just to be able to squeeze through.
Now imagine your flashlight goes out.
Jesus, that's nightmare fuel right there. I nope right out of caving. But I'll be damned if reading about it isn't incredibly exciting.
Don't know where I'm going with this comment. Just read the damn book, ok?
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Well, this should be relevant then:
https://www.amazon.com/Blind-Descent-Quest-Discover-Deepest/dp/0812979494