Learn Hardcore Japanese: ooku no gakusei ha mainiti nihongo wo benkyousimasu.

Here, の works like a connector that turns 多く into something that can directly modify the noun 学生. You can think of it as similar to of in English (many of the students), but in Japanese it is just a normal way to connect this kind of quantity word to a noun.

What is the difference between 多くの学生 and たくさんの学生?

Both basically mean many students, but there are some nuance and usage differences:

多くの学生
- Slightly more formal or written-sounding.
- Common in essays, reports, newspapers.
- Feels a bit more objective or neutral.
たくさんの学生
- More casual and conversational.
- Very common in everyday speech.

In this sentence, you could say:

多くの学生は毎日日本語を勉強します。
たくさんの学生は毎日日本語を勉強します。

Both are correct; the nuance is mostly style (formal vs casual).

Why is は used after 学生 instead of が?

は marks the topic, while が usually marks the subject (or focuses on who/what does the action).

学生は毎日日本語を勉強します。
- 学生 is the topic: As for students, they study Japanese every day.
- The sentence is making a general statement about that group (students).

If you used が:

多くの学生が毎日日本語を勉強します。

This is grammatically correct, but it sounds more like you are identifying or highlighting who it is that does the studying (as opposed to someone else). In many general statements, especially the kind you might see in textbooks, explanations, or broad facts, は is more natural.

Why is there no word like they in the Japanese sentence?

Japanese often omits pronouns (I, you, he, she, they) when they can be understood from context.

In this sentence:

多くの学生 already tells us who we’re talking about.
Japanese does not need to repeat they after that.

So instead of something like:

多くの学生は彼らは毎日日本語を勉強します。 (incorrect / unnatural)

Japanese just says:

多くの学生は毎日日本語を勉強します。

The subject they is understood to be 多くの学生 from context.

Does 学生 mean student or students? There is no plural s.

学生 can mean student or students depending on context. Japanese usually does not mark plural the way English does.

In this sentence:

多くの学生 clearly refers to many students, so 学生 is understood as plural.

If you needed to be very explicit about plurality, you could sometimes use 学生たち, but:

多くの学生たちは… feels redundant or awkward in many contexts.
多くの学生は… is the natural, standard way to say many students.

What is the role of を after 日本語?

を marks the direct object of the verb, the thing that receives the action.

日本語を勉強します。
- 日本語 = Japanese language
- を = direct object marker
- 勉強します = study

So the pattern is:

X を勉強します = study X

Examples:

英語を勉強します。 = I study English.
歴史を勉強します。 = I study history.

Why is there no particle after 毎日?

Time expressions like 今日, 明日, 毎日, 来週 often appear without a particle when they simply state when something happens.

毎日日本語を勉強します。
- 毎日 = every day (time expression, no particle needed)

You can sometimes add に:

毎日に日本語を勉強します。 → This is unnatural.

For 毎日, you normally do not use に.
For specific times, you usually can or must use に:

7時に起きます。 = I get up at 7.
月曜日にテストがあります。 = There is a test on Monday.

Can I change the word order, like 日本語を毎日勉強します or 毎日多くの学生は日本語を勉強します?

Japanese word order is more flexible than English, as long as:

The verb comes at the end.
Particles (は, が, を, に etc.) are attached correctly.

All of these are grammatical:

多くの学生は毎日日本語を勉強します。
多くの学生は日本語を毎日勉強します。
日本語を毎日多くの学生は勉強します。 (grammatical but sounds a bit marked / unusual)

The most natural and neutral in everyday use is usually close to:

多くの学生は毎日日本語を勉強します。
or
多くの学生は日本語を毎日勉強します。

The further you move words away from the most common order, the more emphasis or unusual rhythm you create.

What form is 勉強します, and what is the dictionary form?

勉強します is the polite non-past form of the verb 勉強する (to study).

Dictionary/plain form: 勉強する
Polite form: 勉強します

Basic related forms:

勉強する = (plain) study / will study
勉強します = (polite) study / will study
勉強した = (plain past) studied
勉強しました = (polite past) studied

Does 勉強します mean study, studies, or will study?

Japanese non-past form (like 勉強します, 勉強する) covers both present and future meanings. Context decides.

In this sentence:

多くの学生は毎日日本語を勉強します。

Because 毎日 (every day) shows a habit, 勉強します is naturally understood as:

study (habitual present):
- Many students study Japanese every day.

In another context (without 毎日, talking about a plan), 勉強します might mean will study.

Could I say 勉強する instead of 勉強します in this sentence?

Yes, you can, but the politeness level changes.

多くの学生は毎日日本語を勉強します。
- Polite, suitable for speaking to teachers, strangers, in class, etc.
多くの学生は毎日日本語を勉強する。
- Plain (casual), used in dictionaries, academic writing, or among friends / in informal speech.

Both are grammatically correct.
Choose します for polite speech, する for plain/casual speech or dictionary-style explanation.

Why is 多く before 学生, but 毎日 is before 日本語 (or the verb)? How do I know where to put these?

General patterns:

Words that directly modify a noun go immediately before that noun:
- 多くの学生 = many students
  Here 多くの is like an adjective, so it must be right before 学生.
Adverbs of time/frequency/manner (when, how often, how) usually appear:
- Before the verb, or
- Near the part of the sentence they modify.

So:

毎日日本語を勉強します。
日本語を毎日勉強します。

Both place 毎日 close to the verb 勉強します and are natural.
You cannot say 学生多くの because 多くの must directly attach to 学生.

Is 多く always followed by の, like 多くの学生?

Not always. 多く has two main uses:

多くの + noun
- Acts like an adjective phrase:
- 多くの学生, 多くの人, 多くのお金
- Similar to many students, many people, a lot of money.
Standalone adverb-like use (no の):
- 多く学びました。 = I learned a lot.
- 多くの場合 = in many cases (here it is followed by の, but set phrase).

In your sentence, 多くの学生 is the modifier + noun pattern, so it needs の there.