"I am reading the book even if you hate it."
Translation:Jeg leser boken selv om du hater den.
You would say "..hater du.." if this part of the sentence was dependent on the first part. I can read a book and you can hate it but neither is dependent on the other. If the sentence was "If you hate the book, I will read it" (or something like that), the the second part would end up being "..leser jeg...". Recall the V2 rule--the verb takes the second place of the sentence. The first part of the "If..." sentence takes the first part, then the verb, noun, etc.