Learn Hardcore Korean: jeoneun hangsang doseogwaneseo gongbuhaeyo.

저 means “I” in polite speech, and -는 is the topic marker. Together, 저는 literally means “as for me,” setting the speaker as the topic of the sentence. It’s more respectful than the casual 나는 (나 + -는).

What’s the difference between the topic marker -는 and the subject marker -가?

-는/은 (topic): Introduces what you’re talking about or makes general statements/contrasts (“as for…”).
-가/이 (subject): Identifies the grammatical subject or answers “who/what does it?”
In 저는 항상 도서관에서 공부해요, you’re making a general statement about yourself, so the topic marker -는 is natural.

What does 도서관에서 mean, and why use -에서 instead of -에?

도서관 = “library.”
-에서 marks the place where an action occurs (“at the library”).
-에 alone marks a static location (“in/at the library”) or destination (“to the library”), but doesn’t specifically indicate the site of an action.

What is the role of 항상, and can I move it elsewhere in the sentence?

항상 means “always.” It’s an adverb, so it usually appears before the verb or right after the topic. Both word orders are fine:

저는 항상 도서관에서 공부해요.
저는 도서관에서 항상 공부해요.
The emphasis shifts slightly, but both are grammatical.

Why is 공부하다 written as 공부해요 here?

공부하다 is the dictionary form “to study.” To make it polite present tense:

Remove -다 from 하다.
Conjugate 하다 → 해요.
So 공부하다 becomes 공부해요.

Can I omit 저는 in this sentence?

Yes. Korean often drops the subject/topic when it’s clear from context. You can simply say:
항상 도서관에서 공부해요.
It still means “I always study at the library,” assuming the listener knows you’re talking about yourself.

Is 저는 항상 도서관에서 공부해요 formal or casual? How can I change its politeness level?

This uses the polite -요 ending (friendly/polite).

More formal (plain/polite): 저는 항상 도서관에서 공부합니다.
More casual (informal): 항상 도서관에서 공부해. or 저는 항상 도서관에서 공부해.
Dropping 저는 makes it even more casual if the context is clear.