Aunque es tarde, la biblioteca sigue abierta.

Aunque means although / even though. It introduces a contrast:

• Aunque es tarde = Although it’s late
• la biblioteca sigue abierta = the library is still open

So the whole sentence sets up an unexpected situation: it is late, but the library is still open.

In Spanish, es tarde is the normal way to say it’s late.

Here, ser is used in an impersonal expression:

• Es temprano = It’s early
• Es tarde = It’s late

You do not use estar here.

Here, tarde functions like an adjective in the expression es tarde.

It does not mean afternoon here. Spanish tarde can mean different things depending on context:

• la tarde = the afternoon
• llegar tarde = to arrive late
• es tarde = it’s late

So in this sentence, it clearly means late, not afternoon.

The comma separates the introductory concessive clause from the main clause:

• Aunque es tarde, = although it’s late
• la biblioteca sigue abierta = the library is still open

This is very common and natural in writing. In short sentences, some punctuation choices can vary, but with aunque at the beginning, the comma is standard and helpful.

Spanish uses definite articles more often than English.

So la biblioteca is perfectly natural, even where English might say just the library or simply library depending on context.

In this sentence, la biblioteca refers to the specific library being talked about, so the article is expected.

Seguir + adjective often means to remain / to stay / to continue being something.

So:

• sigue abierta = remains open / is still open

This is a very common structure in Spanish:

• sigue cerrado = it remains closed / it’s still closed
• siguen contentos = they are still happy
• sigo cansado = I’m still tired

Because abierta agrees with la biblioteca, which is feminine singular.

• la biblioteca → feminine singular
• therefore abierta → feminine singular

Compare:

• el museo sigue abierto
• la tienda sigue abierta
• los museos siguen abiertos
• las tiendas siguen abiertas

Adjectives in Spanish usually agree in gender and number with the noun they describe.

Both are possible, but they are not exactly the same.

• Está abierta = it is open
• Sigue abierta = it is still open / it remains open

Seguir adds the idea of continuation. It suggests that maybe you would expect it to be closed by now, but it continues to be open.

That makes it a very good match with aunque es tarde.

Because the subject is la biblioteca, which is singular.

• la biblioteca sigue abierta
• las bibliotecas siguen abiertas

The verb must agree with the subject in number.

Yes, aunque can be followed by either indicative or subjunctive, depending on meaning.

Here we have:

• Aunque es tarde... → indicative

This usually means the speaker presents it’s late as a real, known fact.

If you used the subjunctive:

• Aunque sea tarde...

that could sound more like even if it’s late or even though it may be late, depending on context. It feels less factual or more hypothetical.

So in your sentence, the indicative is used because the lateness is treated as a fact.

Yes. You could also say:

• La biblioteca sigue abierta, aunque es tarde.

This means the same thing: The library is still open, although it’s late.

The difference is mainly focus and rhythm:

• starting with aunque highlights the contrast first
• starting with la biblioteca presents the main idea first

Both are natural.

Historically, it is the feminine form of the participle of abrir (abierto / abierta), but in this sentence it functions as an adjective meaning open.

That is why it agrees with biblioteca:

• abierta with feminine singular
• abierto with masculine singular

In everyday learning, it is usually easiest to think of abierto / abierta here as an adjective.

Yes, you could say:

• Aunque es tarde, la biblioteca continúa abierta.

This is grammatical and understandable. However, seguir + adjective is often the more common and natural everyday choice for still/remain in sentences like this.

So sigue abierta is especially useful to learn as a fixed pattern.