Learn Hardcore Japanese: tosyokan ha eki no tikaku ni arimasu.

は is the topic marker. It sets 図書館 (“the library”) as the topic, telling the listener “we’re talking about the library.” It’s not the same as the subject marker が, which would emphasize or introduce the library as new information. Here, は simply frames the library as the context for the rest of the sentence.

What does the particle の indicate in 駅の近く?

の marks a genitive (possessive/attributive) relationship between nouns. In 駅の近く, it links 駅 (“station”) and 近く (“vicinity”), so it literally means “the vicinity of the station,” i.e. “near the station.”

Why is 近く a noun here, and how is it related to the adjective 近い?

近く is the noun form meaning “vicinity” or “nearby.” The adjective 近い means “close” or “near.” To talk about the location as a noun you attach particles to, you use 近く. That way you can say 駅の近くに (“in the vicinity of the station”).

Why do we add the particle に after 近く?

に marks the location where something exists or happens. Since 近く is a noun meaning “vicinity,” adding に turns it into “in the vicinity,” specifying where the library exists.

Why is the verb あります used instead of います?

Japanese uses あります for the existence of inanimate objects, places, and things. います is used only for animate beings (people, animals). Because a library is an inanimate location, あります is the correct choice.

Could we rephrase the sentence as 駅の近くに図書館があります? What changes?

Yes. By putting 駅の近くに first, you slightly shift the focus to the location (“near the station”) before mentioning the library. The overall meaning (“There is a library near the station”) stays the same. Japanese allows flexible word order as long as the particles remain correct.

What’s the difference between 駅の近くにあります and 駅のそばにあります?

Both 近く and そば mean “near.” そば often implies a closer, almost adjacent proximity, while 近く can be a bit more general (“in the area”). So 駅のそばにあります suggests the library is right next to the station, whereas 駅の近くにあります might mean a short walk away.

How would you say “a library that is near the station” instead of stating its existence?

You can turn the location phrase into a relative clause:

駅に近い図書館 (“station-near library”)
駅の近くにある図書館 (“the library that exists near the station”)
Both use 近い or ある to modify 図書館, forming a noun phrase rather than an existence statement.