Progress! If she looks through the rune dictionary for each of the runes in the invisibility spell (potentially a very useful spell, incidentally), what do they mean? 

They mean lots of random things. Actually, more of them mean random things ("fire") than relevant things ("sight").

Hmm. Each of the runes has multiple words next to it, right? If she traces the diagram very carefully onto a notebook page, and writes in the list of meanings next to each rune, do any patterns jump out? Repeated meanings, more relevant meanings belonging to larger or conversely smaller runes, meanings that seem related for runes that are near each other . . . ?

Lots of repetitions. Most of the irrelevant meanings in the largest batch of runes are repeated in the smaller batch.

She marks up the diagram some more to indicate how the repetitions are arranged spatially. And where are the most relevant meanings found, in terms of rune size and placement?

The single biggest runes are one with a top meaning of "sight" and another with a top meaning of "forbiddance".

That's nice and straightforward, unless it's dangerously misleading. She notetakes about this diagram until there's scarcely a square inch of white paper left on the sheet, then starts in on the next one.

She's still at it five hours in, when she realizes that one, she can barely make her eyes focus on the paper anymore, and two, it's dinnertime. Given her previous success with the lentil soup, she goes to the Avalon's Chinese place for dinner.

It, too, is cheap.

At home, her parents ask her how the park was. She says, "It was nice, I walked around and sat on a bench and read." She goes to bed pretty early for a Saturday, for the luxury of lying in bed in her dragon shape for a while before she has to turn human to sleep.

Sunday is sacrificed to all the homework she didn't do the day before. Monday morning she wakes up early, gets to school right when their doors open, and photocopies as much of the rune dictionary as she can get through before first period.

The runes do not react magically in any way to being photocopied, fortunately.

She's pretty sure you have to chant at them at some point to get anything to happen, and has been careful not to say anything while touching or looking at runes. Still, it's a relief. A few mornings like this should be sufficient to copy the whole dictionary, unless it's a brick.

It has brickish aspirations.

Well, she has these books for a couple of weeks; she can do it with a combination of coming in early and staying after everyone else leaves.

She takes to doing her homework in her bedroom instead of at her kitchen table; that way nobody can tell that it's a mix of hurrying through actual homework and staring at rune diagrams. She knows it should be possible to get where she's going from where she is; from an information-theoretic standpoint all the bits are there. And it's a textbook, it's trying to convey information, it's not like she's trying to access something deliberately encrypted. But she's not a theoretical perfect information-extractor, or even Alan Turing, and she's impaired by her unwillingness to test any of her hypotheses in ways more concrete than "see if they're consistent with all of the diagrams in this book".

The books have no comment on how much information it is theoretically possible to derive from them.

Well, they don't call themselves "A Comprehensive Introduction" or have exercises they expect her to be able to do after reading a certain amount; that's sort of a comment, or at least a very pointed silence. After two weeks she goes back to the Avalon.

It is much as she left it. Different door guard; she has to display her foot again.

Behold: a foot. How's the library doing this fine morning?

It's still there! The librarian recognizes her. "Hello again!"

"Hello! I've got books to return." She hands over the rune dictionary (now redundant with the copy hidden in her desk) and the derivation guide (on which she took detailed notes but which she did not actually copy.) "And I'd like to renew Inscriptions, if nobody else wants it right now."

"Nobody else has it on hold. You're not getting into magic, are you? Nasty dangerous stuff."

"Yes, it does look very dangerous. I've just been reading about the theory; I'd like to learn but I'd rather not try anything until I've got a good solid understanding of what's safe to do and what isn't."

"All right. Just you watch out, don't want to burn your pretty eyebrows off or worse."

"Yes, I'm rather attached to having everything attached. Do you have any books with safety advice, maybe some sort of primer for people who are new to magic?"

"There is one textbook but it's checked out right now, it has been for a while."

"Can I put a hold on it for when it gets back, please?"