Is there an expression or word that describe the action of reading a book very quickly or enthusiastically?
The only thing I can think of besides speed reading (which Hot Licks already suggested) is "skimmed." For example...
She skimmed through the book.
Type "skimmed through the book" into Google and you'll see many examples.
However, skimming doesn't necessarily denote enthusiasm. On the contrary, some people may skim through books they find boring; they simply want to go through it as fast as they can to find something of interest or determine if they want to read it.
If a person is truly interested in a book but wants to read it quickly, he or she will probably stop skimming and get into speed reading mode.
I'd suggest, gobble up
: to read rapidly or greedily
Conceptual Domains and the Acquisition of Metaphor
Table 4 (Continued)
E: The boy gobbled up the book
C: He read it in one whole--he read it--I’m not sure...gobbled up...
E: Do you know what gobbling means? Like when you gobble up food?
C: Yeah--but he couldn’t gobble up (laughs)--I don’t know, he’d have to have an operation (laughs)
E: So what was he doing if he was gobbling up the book?
C: Reading it
"I couldn't put it down." This expression covers the "enthusiastically" part, but not necessarily the "quickly" part.
If you cannot put a book down, you are unable to stop reading it until you reach the end:
It was so exciting from the first page I couldn't put it down.
Tear through (or tear into) might work, as in
He tore through (into) the entire collection of Hardy Boy mysteries.
American Heritage offers this example
To begin to do or eat something with great energy: tore into the meal.
Also lapped up is heard.
(I note that many of the offered answers use food analogies.)