This is the 9363rd most frequent Russian word.
тартуcкая
The word "тартуская" refers to something related to Tartu, a city in Estonia.
Тартуская is used here as an adjective describing architecture related to Tartu.
Я изучал тартуская архитектура во время моего отпуска.
I studied Tartu architecture during my vacation.
Тартуская is an adjective here, indicating cultural aspects associated with Tartu.
Тартуская культура очень богата и разнообразна.
Tartu culture is very rich and diverse.
Тартуская modifies 'кухня', indicating cuisine from or inspired by Tartu.