largest part звучит предпочтительней biggest part. Но оба имеют смысл, если книга разделена на части. А так - лучше "... most of the book..."

Да, Alex, Вы правы, спасибо.

She would HAVE read most of the book by the next week.

Good catch, Al, this sentence is begging for the perfect.

Why can't it refer to the future? We don't know the context.

Can you give her this book? If you could give her this book she would read a good portion of it by the next week and be ready for the discussion.

Then it would “she will have read ...”

She will have read - она прочитает
She would read - она бы прочитала
Разве не так?

If it’s hypothetical, you can say “If you had given her the book, she would have read a good portion of it by next week.”

This relates to what hasn't happened (упущенная возможность)
But if I want to say about what could happen in future, if you gave her the book, there's no need to use the Perfect Tense... ???

It's Conditional 2

Oh, I see what you mean: "If you were to give her the book, she would read a good portion of it by next week."

But is my interpretation also possible in the right context?

Can you give her this book? If you could give her this book she would read a good portion of it by the next week and be ready for the discussion. But I know you are meanie and will never give her this book.

Of course, your interpretation is possible when we talk about the past, the lost opportunity.

In that case, “...if you GAVE her this book”

COULD GIVE doesn't work? Why?

Here are examples with "could do smth" in these types of sentences: http://learnenglish.britishcouncil.org/en/quick-grammar/conditionals-1

Elena, you told me you intended this to be the second conditional, which requires a past tense verb. I don't understand why you're using COULD. I would have written: "WOULD you give her this book? If you GAVE her this book she would read a good portion of it by next week and be ready for the discussion. But I know how stingy your are and will never give her the book." COULD is more about his ability to give the book than his WILLINGNESS to give the book.

OK, clear with COULD, but the idea is correct. Thank you, Uly! :)

Yes, very good)