Russian does the same thing, though in a more detailed fashion. Like in all Russian cases, adjectives will agree with the noun they modify and go into the same case. Now for some case charts. Immediately below are singular nouns as examples. Note that the word in the middle is in the nominative, the word on the right is in the genitive singular.
All endings can vary between hard and soft variants depending on the consonant.
Now for the genitive plural of nouns. These endings are the same as the accusative plural of animate nouns. This is the most complicated set of endings in Russian. In the tables below is a summary of the adjective endings and how they change. After the number one, the adjective and the noun which follow are in whatever case is required by the sentence.