Of the city, of my brother (центр города)

The Of-Phrase

You already know у + Genitive for owning things: У брата есть машина. — My brother has a car. Russian has a second, even simpler use of the same case: put one noun after another and the second — in the Genitive — tells you whose or of what.

phraseliterally
центр городаthe centre of the city
машина братаthe car of my brother — my brother's car
дверь домаthe door of the house
фото сестрыa photo of my sister

No preposition, no verb — the case ending alone does the work of English of and 's.

This is the centre of the city.
Это центр города.

Order Matters

The thing comes first, the owner second: машина брата is the brother's car; брат машины is nonsense. Whatever English does with its apostrophe, Russian always says the thing of the owner.

Over there is my brother's car.
Там машина брата.

Same Endings You Already Know

The endings are the ones this level just taught: -а/-я for masculine and neuter (город → города, море → моря), -ы/-и for feminine (сестра → сестры, песня → песни).

The window of the room is big.
Окно комнаты большое.

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