This is the 4881st most frequent Russian word.
итальянским
The word "итальянским" is the instrumental or dative case form of the adjective "итальянский," meaning "Italian" in English.
Here, 'итальянским' is an adjective in instrumental case, modifying 'искусством' (art) to describe art that is related to Italy.
Я увлекаюсь итальянским искусством.
I am fond of Italian art.
In this sentence, 'итальянском' refers to the Italian language and is in the prepositional case as it follows the preposition 'на' (in).
Мы разговаривали на итальянском вчера вечером.
We spoke in Italian yesterday evening.
The word 'итальянском' is in the prepositional case, modifying 'стиле' (style), and describes a style characteristic of Italy.