I'm absolutely no specialist on tarot history but here are some books I liked, found interesting and learned from.
I liked Robert Place's book "The Tarot: History, Symbolism, and Divination", and Cynthia Giles' "The Tarot: History, Mystery and Lore" which is a bit older but many newer books seem to be built upon it. Place's books are all excellent and well researched, far as I can see.
A very useful resource on Renaissance influences on the tarot is Brian Williams' companion book to his Renaissance tarot. I'm re-reading it and enjoying it. It gives the history of tarot images in the context of the Renaissance.
Mary Packard's "The Golden Tarot: The Visconti-Sforza Deck" is a good introduction to this historical deck (I bought the LoS deck many years ago and the book separately here on AT), and Yoav Ben Dov's "Tarot - the Open Reading" is helpful in reading the Marseilles deck.
That's it from my limited book shelf ;-)