tosyokan no sangai de nihongo wo benkyousimasu.

A natural reading is:

としょかん の さんがい で にほんご を べんきょうします。

In rōmaji, that is:

Toshokan no sangai de Nihongo o benkyō shimasu.

A few useful reading notes:

• 図書館 = としょかん (library)
• 三階 = さんがい (third floor)
• 日本語 = にほんご (Japanese language)
• 勉強します = べんきょうします (study)

Notice that を is written を but pronounced like お in modern Japanese.

の connects nouns.

Here, 図書館の三階 means the third floor of the library or the library’s third floor.

So:

• 図書館 = library
• 三階 = third floor
• 図書館の三階 = the third floor of the library

A very common pattern is:

A の B = B of A / A’s B

Examples:

• 学校の先生 = the school’s teacher / teacher at the school
• 日本の文化 = Japanese culture / the culture of Japan

で marks the place where an action happens.

In this sentence, the action is 勉強します (study), so 三階で means on the third floor as the location where the studying happens.

Compare:

• 図書館の三階で勉強します。 = I study on the third floor of the library.
• 公園で食べます。 = I eat in the park.
• 教室で話します。 = I speak in the classroom.

So here, で is basically saying at/in/on the place where the action occurs.

This is a very common question.

Both で and に can relate to places, but they do different jobs.

• で = where an action takes place
• に = destination, existence, or a specific point in time

Since studying is an action happening at that location, で is correct:

• 図書館の三階で勉強します。 = study on the third floor

If you used に, it would not sound right for the place of this action.

Compare:

• 学校に行きます。 = go to school
  (に marks destination)
• 学校で勉強します。 = study at school
  (で marks location of action)

を marks the direct object of the verb.

Here, the verb is 勉強します (study), and the thing being studied is 日本語 (Japanese).

So:

• 日本語を勉強します = study Japanese

This is the basic pattern:

object を verb

Examples:

• 本を読みます。 = read a book
• 音楽を聞きます。 = listen to music
• 日本語を話します。 = speak Japanese

In modern pronunciation, を usually sounds like お, even though it is written を.

Because Japanese normally uses Subject-Object-Verb word order, and the verb usually comes at the end of the sentence.

In English, you say:

• I study Japanese on the third floor of the library.

In Japanese, the structure is more like:

• [library’s third floor] [at] [Japanese] [object marker] [study]

So the verb 勉強します comes last.

This is one of the biggest word-order differences between English and Japanese.

Yes, the subject is omitted, and that is very normal in Japanese.

If the context already makes it clear who is doing the action, Japanese often leaves out words like:

• I
• you
• he/she
• we

So 図書館の三階で日本語を勉強します。 can mean:

• I study Japanese on the third floor of the library
• We study Japanese on the third floor of the library
• or another subject, depending on context

If you wanted to include I, you could say:

• 私は図書館の三階で日本語を勉強します。

But very often, Japanese does not state 私は unless it is needed for clarity or contrast.

勉強します is the polite non-past form.

It can mean:

• study (habitually / generally)
• will study (future)
• sometimes am going to study, depending on context

Japanese does not have a separate future tense the way English does. The non-past form can refer to present habits or future actions.

Examples:

• 毎日勉強します。 = I study every day.
• 今日は勉強します。 = I will study today.

Also, 勉強 is a noun, and します is the verb to do, so this is a very common noun + します pattern:

• 勉強します = do study / study
• 運動します = exercise
• 仕事します = work

Because 勉強する is a suru-verb.

Many Japanese verbs are made from:

• a noun-like word
• plus する (to do)

So:

• 勉強 = study (as a noun/concept)
• する = to do
• 勉強する = to study
• 勉強します = polite form of 勉強する

This pattern is extremely common:

• 練習する = to practice
• 質問する = to ask a question
• 旅行する = to travel

Yes, Japanese word order is more flexible than English, as long as the particles stay correct.

For example, these are both natural:

• 図書館の三階で日本語を勉強します。
• 日本語を図書館の三階で勉強します。

Both mean basically the same thing. The difference is mostly about emphasis or flow.

However, the verb usually still comes at the end:

• 勉強します stays last

The particles で and を are what show each word’s role, so Japanese does not depend on word order as much as English does.

Because 階 often changes pronunciation in compounds.

By itself:

• 階 is commonly read かい

But after some numbers, sound changes happen, and the reading becomes easier to pronounce naturally.

For floors:

• 一階 = いっかい
• 二階 = にかい
• 三階 = さんがい
• 四階 = よんかい
• 五階 = ごかい

So 三階 is correctly read さんがい.

This kind of sound change is common in Japanese, so it is often best to learn common combinations as full vocabulary items.

Yes, that is a helpful way to think about it.

• 日本 = Japan
• 語 = language

So:

• 日本語 = Japanese language
• 英語 = English
• 中国語 = Chinese
• 韓国語 = Korean

The kanji 語 is often used for languages.

Yes. That would simply mean:

I study Japanese at the library.

The phrase の三階 adds more detail:

• 図書館で日本語を勉強します。 = I study Japanese at the library.
• 図書館の三階で日本語を勉強します。 = I study Japanese on the third floor of the library.

So 図書館の三階 is a more specific location inside the library.

It is polite, because it uses 勉強します.

Japanese commonly has:

• polite style: 勉強します
• plain/casual style: 勉強する

So:

• 図書館の三階で日本語を勉強します。 = polite
• 図書館の三階で日本語を勉強する。 = plain/casual

The polite form is very common in textbooks and when speaking respectfully or neutrally.