Breakdown of Bardzo podoba mi się sztuka.
bardzo
very
podobać się
to appeal / to like (aesthetically, first impressions)
mi
to me
sztuka
art
Questions & Answers about Bardzo podoba mi się sztuka.
Why isn't there a word for "I" (like ja) in this sentence?
When you use podobać się to say you like something, the grammar works backward compared to English. The thing you like is the subject, and it is "pleasing to" you. Instead of "I like art", you are literally saying "Art is very pleasing to me." The word mi means "to me".
Since the sentence translates to "I like", why is the verb podoba instead of podobam?
Because you are not the one doing the action. Since the literal meaning is "Art is pleasing to me", the verb has to match "art" (sztuka). Sztuka is a "she/it" noun, so we use the third-person singular form podoba.
What case is sztuka in here? Does it change?
It is in the nominative case, which is the basic dictionary form. It does not change because it is the grammatical subject of the sentence. Even though it comes at the end, sztuka is the thing doing the action of "being pleasing."
Could I change the order and say Bardzo podoba się mi sztuka?
That would sound unnatural. Both mi and się are short, unstressed words that usually cluster together after the verb. When they cluster, a personal pronoun like mi almost always comes right before się.