This is the 15042nd most frequent German word.
serbischer
"Serbischer" means "Serbian" (relating to Serbia or its people).
The word 'serbischer' is used to denote an adjective ('Serbian') referring to the subject 'culture', yet the ending 'er' should agree with the case; the correct form is 'serbische' for this sentence.
Ich lese ein Buch über serbischer Kultur.
I am reading a book about Serbian culture.
The word 'serbischer' is an adjective ('Serbian') modifying 'Trainer' (coach). It is used as a predicate adjective in this nominative case sentence.
Der serbischer Trainer gewann den Preis.
The Serbian coach won the prize.
The word 'serbischer' describes as an adjective ('Serbian') the noun 'Restaurant'; however, the ending should reflect the accusative neuter case, making 'serbisches' the correct choice.