O kitabı okudum.

Did I necessarily finish the book?

Once I´ve heard it is possible to use the locative case to indicate that you read the book partially, just a piece. And then it is like: Kitapta okudum. 

But I am not very sure it is right

Yeah it gives such a meaning. 

Kitap okudum. (I read book.) [simp.past]

kitap+ı(accusative)

Kitabı okudum. (I read the book.)

Yes. You have finished the book.

kitap+da(locative)---->kitapta (in/at the book)

Kitapta okudum. (I read in the book.)

Şimdi anlattığın hikâyeyi bir kitapta da okudum. (I read the story you have been telling now in a book too.)

Yeah, that´s the common Locative meaning.. I must have confused something... Perhaps it was a different case? Again, is there something like Kitaptan okudum to mean not only "I read from the book", but "I read the book partially"?

Thank you all the three of you. (Mehmet knows Finnish, he probably knows why I asked...)

Evet. Doğru düşünmüşsün. (Yes. You have thought true.)

Kitaptan okudum. (1I read the book. 2(explaining translation) I arrived this text/knowledge etc. via the book.

another examples for the meaning of "via" with ablative case:

e-posta (e-mail)

Makalenin PDF´sini bana Facebook´tan gönderme; e-posta adresimi vereyim, oradan gönder

(Don´t send me the PDF of the essay via Facebook, let me give my e-mail adress and send it via there.)

Sana bunu telefondan anlatamam, yüz yüze konuşmamız gerek.(I can´t tell you this on* the phone, we need to talk face to face.)

*I can´t tell this to you [talking] via telephone. (direct)