I’ve finished reading the book.
Would this really be understood in German to mean “I read the book to the end”? It looks more like “I stopped reading the book” (aufhören = to stop), in the sense of “I didn’t like this book, so I’m not going to read it to the end”.
I would have expected something more like “Ich habe das Buch bis zum Ende gelesen” given Clozemaster’s suggested English translation.
I understand it completely in the same way as you do.
“I’ve stopped reading the book” implicit “without finishing it” =
“Ich habe mit dem Lesen des Buches aufgehört” (ohne es zu Ende zu lesen).
Gut beobachtet!
I totally agree, the translation does not match, and I would interpret the german the same way.
Your suggested translation is good, but a bit verbose compared to the english one.
For something shorter, how about:
Ich bin mit dem Buch fertig.
Ich bin mit dem Buch durch.
Ich habe das Buch durch.
Ich habe das Buch durchgelesen.
Ich habe das Buch fertig gelesen.
Ich habe das Buch zuende gelesen.