It helps when you see that this article is actually an excerpt from a book, without that knowledge the sentence doesn’t really parse.

Ah, that's it, thanks! For some reason I was thinking "this little book" was Darwin book (that it's actually quite small).

Not a native speaker either but it seems like an acceptable sentence. Here is a slightly reworked version that might be easier to understand. The brackets mark where I added something or left something out:

"I am sure that many [...] readers of this [...] book know [the book] 'On the Origin of Species' (by Charles Darwin) inside and out."

Edit: "to know something inside and out" means to be very familiar with something.

The book is the book that the article is an excerpt from, not Darwin's.

From my point of view this is still clear in the shortened sentence.

Well, I'm also not a native speaker, but it makes sense to me. Author is implying that every reader of his book knows "On the Origin of Species" very well.

I mean ... I get what he's saying but no, it's not well written and it's tautological. Since erudite literally means having a deep knowledge:

"I am sure many experts on X know X inside out"

Erudite may be referring to generally well-read. Anyway, the sentence reads ok to me fwiw.

I'd agree, except it reads to me as "many of the erudite readers _of this_ little book", it seems to imply erudites of Darwin's book.

"this little book" refers to "The Nation of Plants" - from which this piece is an excerpt. It's probably more obvious when you're holding the book, as opposed to reading an excerpt on the internet.

Well, in that case I stand corrected :) It makes sense.

looks right. You could re-write it as follows for clarity: "I am sure that many of you are familiar with Darwin's book On the Origin of Species"