Learn Turkish: Bu kitabın yazarı çok genç. - The author of this book is very young.

This is a definite noun compound, which links an owner and an owned thing. The first word (kitap) gets the genitive suffix -ın to mean "of the book", and the second word (yazar) gets the third-person possessive suffix -ı to mean "its author". Together, they form "the author of the book".

Why is it kitabın with a "b" instead of kitapın?

This happens because of consonant mutation. When a Turkish word ends in a hard consonant like p, ç, t, or k (often remembered as the "ketçap" rule), and you add a suffix starting with a vowel like -ın, that hard letter softens. Here, the p in kitap turns into a b.

Does the word Bu ("this") describe the book or the author?

It describes the book. In Turkish, a describing word always goes right before the noun it belongs to. Because it sits right in front of kitabın, it means "of this book". If you wanted to say "This is the author of the book", you would pause and separate it with a comma: Bu, kitabın yazarı.

Where is the word for "is" in this sentence?