Learn Hardcore Russian: Я хочу оформить аренду квартиры в центре города. - I want to arrange the rental of an apartment in the city center.

снять квартиру – the most common everyday way to say “to rent an apartment” (from the tenant’s point of view).
- Я хочу снять квартиру в центре. – I want to rent an apartment in the center.
арендовать квартиру – more formal, bookish, often used in written language, contracts, business contexts.
- Я хочу арендовать квартиру. – I want to rent (lease) an apartment.
оформить аренду квартиры – literally “to formalize the rental (lease) of an apartment”: focus on the paperwork / legal procedure, not just the idea of living there.
- It implies signing a contract, registering the rental, doing documents.

So your sentence Я хочу оформить аренду квартиры в центре города suggests: > I want to take care of the formalities / paperwork to rent an apartment in the city center,
not just “I’d like to rent a place there.”

Why is аренду in that form? What case is it, and why?

Аренду is the accusative singular of аренда (feminine noun, “rent / rental / lease”).

Rule:

The verb оформить (“to formalize, to process, to arrange (officially)”) takes a direct object in the accusative.

So:

оформить (что?) аренду – to formalize what? the rental → аренду (accusative).

Nominative: аренда
Accusative: аренду

Why is it аренду квартиры and not аренду квартиру?

Because in Russian, when you say “rental of something”, you normally use a noun + noun structure:

аренда квартиры – “rental of an apartment”
аренда машины – rental of a car
аренда офиса – rental of an office

Here:

аренду – accusative (what are we formalizing?)
квартиры – genitive singular (of what? of an apartment)

So the pattern is:

оформить аренду (чего?) квартиры
to formalize the rental (of what?) – of an apartment

Аренду квартиру would be ungrammatical in this meaning.

What case is квартиры, and why is it used here?

Квартиры is genitive singular of квартира.

It appears because аренда (“rental”) often governs a genitive noun to show possession / “of” relationship:

аренда квартиры – rental of an apartment
аренда дома – rental of a house
аренда помещения – rental of premises

So the structure is:

аренда (чего?) квартиры – genitive to show “of an apartment”.

What does оформить add that снять doesn’t?

снять квартиру focuses on the practical action of renting to live there.
оформить аренду квартиры focuses on formalizing, registering, or completing official paperwork for the rental.

If you say:

Я хочу снять квартиру в центре города.
→ I want to find and rent an apartment (and live there) in the city center.
Я хочу оформить аренду квартиры в центре города.
→ I want to deal with the official arrangements / contract for an apartment in the city center.

In normal everyday speech about just finding a place to live, people usually say снять квартиру, not оформить аренду квартиры.

Why is the verb оформить perfective, not оформлять?

Russian uses:

Perfective (оформить) for a single, complete result:
- Я хочу оформить аренду. – I want to complete the formalization / get it done.
Imperfective (оформлять) for ongoing / repeated / process:
- Я хочу оформлять аренду квартир. – I want to be engaged in processing apartment rentals (as an ongoing activity, e.g., as a job).

In your sentence, the speaker wants to finish one particular action (get the contract done), so оформить (perfective) is natural.

Can I drop я and just say Хочу оформить аренду квартиры…?

Yes, and it’s very common in spoken Russian.

Я хочу оформить аренду квартиры в центре города.
Хочу оформить аренду квартиры в центре города.

In the second sentence, the subject я is understood from the verb form (хочу is 1st person singular). Dropping я makes the sentence a bit more informal or “streamlined,” but it’s still completely correct.

Can I change the word order, for example: Я хочу в центре города оформить аренду квартиры?

Yes, Russian word order is flexible. Different orders are possible, with small changes in emphasis:

Я хочу оформить аренду квартиры в центре города.
– Neutral: “I want to formalize the rental of an apartment in the city center.”
Я хочу в центре города оформить аренду квартиры.
– Emphasis a bit more on where you want to do this: specifically in the city center is where you intend to do the paperwork.
Оформить аренду квартиры в центре города я хочу.
– More unusual, stylistic, puts strong emphasis on the whole оформить аренду… phrase.

The first version is the most standard and natural in neutral context.

What case is в центре города, and why are there two different endings, -е and -а?

В центре города is a combination of:

в центре – “in the center”
- центр in prepositional case: в центре → “in the center”
города – “of the city”
- город in genitive case: города → “of the city”

So literally:

в центре города = “in the center of the city”

Pattern:

When you say “center of something”, Russian usually uses центр + genitive:
- центр города – the center of the city
- центр Москвы – the center of Moscow

And “in the center of” becomes:

в центре города / Москвы / Парижа (prepositional + genitive).

Could I just say в центре without города?

Yes:

Я хочу оформить аренду квартиры в центре.

This is perfectly grammatical. The difference:

в центре города – explicitly “in the center of the city”
в центре – depends on context; usually still understood as “in the center (of town / of the city)” if nothing else is specified.

In many everyday situations, people simply say в центре, unless they need to distinguish it from the center of some other place.

How would I say “I want to rent an apartment in the city center” in a simpler, very common way?

The most common everyday version is:

Я хочу снять квартиру в центре города.

You can also say:

Я хочу снять квартиру в центре.

Both are very natural for “I want to rent an apartment in the city center,” focusing on finding a place to live, not on the formal paperwork.

Is there any difference between “apartment” vs “flat” in Russian, like in English?

No. Russian uses one word for both: квартира.

Whether in American English it would be “apartment” or in British English “flat,” in Russian it’s квартира.

просторная квартира – a spacious apartment / flat
снять квартиру – rent an apartment / flat

How do I know that квартира and аренда are feminine, and how does that affect the endings here?

Both nouns end in -а in the basic dictionary form:

аренда – rental
квартира – apartment

Most nouns ending in -а / -я are feminine, so their declension patterns are similar.

Relevant forms:

Аренда (feminine):

Nominative: аренда (Что это? – аренда.)
Accusative (direct object): аренду (оформить аренду)

Квартира (feminine):

Nominative: квартира (Что это? – квартира.)
Genitive: квартиры (нет квартиры; аренда квартиры)

So in your sentence:

аренду – accusative feminine singular
квартиры – genitive feminine singular

Their gender is reflected in these endings.

Does Russian have anything like English articles “a / an / the” in this sentence?

No, Russian doesn’t use articles at all. There’s no direct equivalent of “a / an / the”.

The phrase аренду квартиры can mean:

“the rental of an apartment”
“the rental of the apartment”

Which one you choose in English depends on context, not on any explicit word in Russian. In your sentence, it would most naturally be understood as “an apartment in the city center”, unless the context clearly points to a specific known apartment.