Someone please correct me if I'm wrong, but isn't the possessive also used to create compound words, i.e. "kitabın yazarı" could also be translated as "book author" ("Buchautor" for the German speakers), and not just as "book's author"? Or would "book author" be simply "kitap yazar" in Turkish?
Almost. The third person singular possessed ending -(s)i(n) is used to create compound words without using the possessor marking on the initial noun. So:
taksinin şöförü = the driver of the taxi [possessor and possessed marked]
taksi şöförü = taxi driver [only the main noun of the compound phrase marked]
So yes, kitap yazarı is a meaningful phrase. It struck my eye as just a bit strange since I don't normally feel the need to modify yazar but it would certainly have its contexts. I don't think Turkish goes for the compound word quite as often as German, but then, most languages outside of Sanskrit don't.:)
Here you have a Genitive (possessive) construction: Two words are linked with each other
-The owner : gets (n)ln ending - in this case: Kitabın -of the book (no 'n' because kitaP ends with a consonant, ı- for the the 'a' in kitAp (vowel-harmony))
-The possessed: gets s (l) (n) ending - in this case: yazarı -the author (no 's' because yazar ends with a consonant, 'ı' for the the 'a' in yazAr (vowel-harmony) no 'n' -because there is no other case ending (like for instance accusative) to be attached)
Now we have 'the author of the book'.
-'Your book' would be: With the same structure as above 'Sen-İN kitab-İ' -Next step is to glue them together: (sen-İN) kitab-İ + Kitabın yazarı = ? - we drop the pronoun 'senim ' and take only the second part of the term kitab-İ (your book) + (n) because we have another ending following+ the possessive ending (ın) of our second term (Kitabın yazarı)=
Kitabının yazarı - the author of your book.
(I am only a learner, so I hope I got it right)