まだ本を読んでいません = I still haven’t read the book
まだ本を読みません = I won’t read the book for a while
The technical definition of まだ is “some state that existed in the past still remains” – which you translate as “still” or “yet”. In the first sentence, the state of “not having read the book” is still present now (読んでいない), while in the second sentence, the state will be continuing for the foreseeable future (読まない).
When you use たくさん, “still haven’t” is pretty much the only usage that makes sense, so 読んでいない.
And I’m hoping that explanation didn’t just confuse matters further. =P