Learn Hardcore Japanese: hutuu no hi ha tosyokan de benkyousimasu.

の links a noun to another noun: X の Y = “Y that is X.”
普通 is primarily a noun (and often treated as a “no-adjective”). With の, it modifies 日: 普通の日 = “a normal/ordinary day.”
You will almost always say 普通の before a noun. 普通な日 is possible but uncommon; stick with 普通の日.
Related forms:
- Predicate: それは普通だ。 “That’s normal.”
- Adverb: 普通に “normally; in a normal way” (also colloquially “quite/rather” in some contexts).

Why is は used after 日? Why not に?

は marks the topic: “As for normal days, …” It often carries a contrastive feel (vs. weekends, holidays, etc.).
に marks a specific point in time. You can use it here, but the nuance shifts.
- 普通の日は図書館で勉強します。 Topic/contrast: On normal days (as opposed to other times), I study at the library.
- 普通の日に図書館で勉強します。 Time marker, more neutral: I study at the library on normal days.
- 普通の日には図書館で勉強します。 Stronger emphasis/contrast by combining both.
Many routine time expressions can drop に altogether (e.g., 毎日, 週末).

Could I say 普段は instead of 普通の日は? What’s the difference?

普段は means “usually/as a rule,” focusing on your general habit: 普段は図書館で勉強します。
普通の日は literally means “on normal/ordinary days,” implying “on days that aren’t special (e.g., not holidays).”
If you specifically mean weekdays, say 平日は.

Why is で used with 図書館? Could I use に?

で marks the location where an action is performed: 図書館で勉強します = “study at the library.”
に marks a destination or location of existence. Use に with motion verbs (行く, 来る) or existence (ある, いる):
- 図書館に行きます。 “I go to the library.”
- 図書館にいます。 “I’m at the library.”

Is 図書館に勉強します correct?

No. Use 図書館で勉強します for “study at the library.” If you want “go to the library to study,” use the purpose construction:

図書館に勉強しに行きます。 or 図書館に勉強に行きます。

Where is the subject? Should I add 私は?

Japanese often omits the subject when it’s clear from context. Here, it’s understood as “I.” Adding it is fine, especially if you’re introducing yourself or contrasting:

私は普通の日は図書館で勉強します。 Multiple topics with は (私は… 普通の日は…) are common and natural.

What tense/aspect is 勉強します? Does it mean “I study” or “I will study”?

勉強します is non-past polite. It covers:

Habitual/general: “I study (as a routine).”
Scheduled/near-future: “I will study.” With a habitual time phrase like 普通の日は, it’s read as a routine.

Can I say 勉強しています instead? How does that change the nuance?

勉強しています is the progressive/continuous form.

普通の日は図書館で勉強しています can imply an ongoing arrangement or current habit (“these days, on normal days, I’ve been studying at the library”). It feels a bit more “in progress/these days” than the simple habitual 勉強します.

Is the word order fixed? Can I move things around?

Japanese word order is flexible, but the usual flow is “time > place > action.”

Natural: 普通の日は、図書館で勉強します。
You can topicalize other parts if you want to contrast them:
- 図書館では、普通の日は勉強します。 (contrast “at the library” with other places) Keep で directly marking the place; don’t drop it or separate it far from the verb.

Can I omit any particles here?

In casual speech, you might hear 普通の日、図書館で勉強します (dropping one は), but keeping は is clearer, especially for learners.
Do not drop で; it’s needed to mark the action location.

How do I pronounce the sentence?

Kana: ふつうのひはとしょかんでべんきょうします。
Romaji: Futsū no hi wa toshokan de benkyō shimasu. Note the long vowels in futsū and benkyō.

If I meant “on weekdays,” should I use 平日?

Yes:

平日は図書館で勉強します。 = “On weekdays, I study at the library.” This is more precise if you’re contrasting weekdays with weekends.

What’s the difference between 図書館 and 図書室?

図書館: A library (public, university, etc.).
図書室: A “library room” or reading room, often a smaller facility inside a school or company.

Could I say 普通は図書館で勉強します? How is that different from 普通の日は?

普通は図書館で勉強します。 = “Generally/usually, I study at the library.” It describes your usual practice overall.
普通の日は図書館で勉強します。 = “On normal days, I study at the library.” It frames it by the type of day (not a special day), inviting contrast with weekends/holidays/special occasions.