This is the 16451st most frequent Russian word.
русской
"Русской" is the feminine dative or instrumental form of "русский," meaning "Russian" (relating to Russia or its people/language).
In this sentence, 'русской' serves as an adjective in instrumental case modifying 'культурой', expressing the characteristic of the noun in action.
Она русской культурой увлекается.
She is fond of Russian culture.
Here, 'русской' is an adjective in dative case modifying 'истории', identifying the origin or theme of the noun.
Эта книга посвящена русской истории.
This book is dedicated to Russian history.
In this sentence, 'русской' is an adjective in genitive case modifying 'натуры', indicating possession or association.