В метро шумнее, чем в библиотеке.

Russian normally omits the verb to be in the present tense.

So:

• В метро шумнее literally means In the metro, [it is] noisier
• чем в библиотеке = than in the library

A more literal breakdown is:

• В метро = in the metro
• шумнее = noisier
• чем = than
• в библиотеке = in the library

English needs is, but Russian does not here.

Шумнее is the comparative form meaning noisier.

It comes from шумно (noisily / it is noisy) or is closely related to шумный (noisy). In this sentence, it functions like it is noisier rather than directly describing a noun.

So:

• шумно = noisy / it is noisy
• шумнее = noisier / it is noisier

This sentence is really about the noise level in a place, not about a specific object being noisy.

Чем is the usual word for than in comparisons.

So:

• шумнее, чем... = noisier than...
• быстрее, чем... = faster than...
• интереснее, чем... = more interesting than...

In this sentence:

• В метро шумнее, чем в библиотеке.
• It is noisier in the metro than in the library.

Both phrases use в to mean in, and both are talking about location, so they use the prepositional case.

But the nouns behave differently:

• метро is an indeclinable noun, so it stays метро
• библиотека is a regular noun, so in the prepositional case it becomes библиотеке

So:

• в метро = in the metro
• в библиотеке = in the library

This is very common in Russian: some borrowed nouns like метро, кино, кафе often do not change form.

В is used because the sentence is about being inside / in a place.

Here it means:

• в метро = in the metro / on the subway
• в библиотеке = in the library

Russian often uses в where English might sometimes say in, at, or even on, depending on the place.

For example:

• в школе = at school / in school
• в магазине = in the store
• в метро = in the metro / on the subway

So the exact English translation may vary, but в is the natural Russian preposition here.

Because this sentence describes location, not motion.

Compare:

• в библиотеке = in the library → location
• в библиотеку = into/to the library → motion toward it

In your sentence, nobody is going anywhere. It is just comparing two places:

• In the metro, it is noisier than in the library.

So Russian uses the prepositional case:

• в библиотеке

not the accusative:

• в библиотеку

Yes, более шумно is grammatically possible, but шумнее is more natural and common here.

Compare:

• В метро шумнее, чем в библиотеке. → the normal, natural version
• В метро более шумно, чем в библиотеке. → also understandable, but less simple and less idiomatic in everyday speech

Russian often prefers the simple comparative when it exists:

• быстрее rather than более быстро
• тише rather than более тихо
• шумнее rather than более шумно

For a learner, the safest way to understand it is that шумнее here behaves like a predicative comparative: it describes the general condition of the place.

So the idea is not:

• the metro is a noisier thing

but rather:

• it is noisier in the metro

That is why this pattern often feels closer to English it is noisy / noisier.

A useful parallel:

• В комнате тихо. = It is quiet in the room.
• В комнате тише, чем на улице. = It is quieter in the room than outside.

Literally, it is:

• В метро = in the metro
• шумнее = noisier
• чем = than
• в библиотеке = in the library

So: In the metro, [it is] noisier than in the library.

This word order is very natural in Russian. It puts the place first and then says what it is like there.

Yes, Russian word order is flexible, but the original version is the most neutral and natural.

For example, you may also hear:

• Шумнее в метро, чем в библиотеке.

This still means the same thing, but it gives a slightly different emphasis.

The original:

• В метро шумнее, чем в библиотеке.

is a straightforward way to compare the two places.

Russian has no articles like a or the.

So:

• в метро can mean in the metro
• в библиотеке can mean in the library

Whether English uses a, the, or no article at all depends on context and on normal English usage, not on a separate Russian word.

The stress is on the second syllable:

• шумнЕе

A rough guide for an English speaker:

• shoom-NYE-ye

The ее sequence can be tricky, so listen carefully to native pronunciation if you can. The important point is that the stress falls on -не-:

• шумнЕе

not on the first syllable.