Wanted to throw in a couple of books that I think did a nice job covering the History of Tarot, but were actually books about certain decks.
The first is Robert Place's "The Tarot of the Saints", which I thought gave an excellent overview of the many possible influences of Tarot, and is a nice deck as well.
The second is "Art and Arcana: Commentary on The Medieval Scapini Tarot" by Ronald Decker. Decker is one of the most respected Tarot Historians around, and his book to accompany the Medieval Scapini is full of interesting information. You can buy it seperately from the deck.
Third, the book that comes with the set of the Lo Scarabeo version of the gold "Visconti Tarots", book by Giordano Berti. Lots of good info about our earliest surviving examples of Tarot Decks.
best,
robert