This is the 783rd most frequent Ukrainian word.
київській
Relating to Kyiv.
In this sentence, "Київській" is used as an adjective indicating that the library is located in Kyiv.
Я навчаюсь в Київській національній бібліотеці.
I study at the Kyiv National Library.
Here, "київській" describes the apartment as situated in the city of Kyiv.
Моя бабуся проживає в київській квартирі.
My grandmother resides in a Kyiv apartment.
In this usage, "київській" attributes the academy as being associated with Kyiv.