kinou ha tosyokan no zisyuusitu de nihongo wo benkyousimasita

は marks きのう as the topic of the sentence. It gives the sense of as for yesterday or simply sets the time frame.

So:

• きのうは = yesterday / as for yesterday

In natural English, we usually just say Yesterday, I studied Japanese..., but in Japanese, は helps organize the sentence by introducing what the sentence is about.

Time words like きのう (yesterday), きょう (today), and あした (tomorrow) usually do not take に.

So you normally say:

• きのう勉強しました
• きのうは勉強しました

not:

• きのうに勉強しました ✗

A rough rule:

• Use に with specific points in time such as 3時に, 月曜日に, 2024年に
• Do not usually use に with relative time words like きのう, きょう, あした

の connects nouns. Here it shows that the self-study room belongs to or is associated with the library.

So:

• 図書館 = library
• 自習室 = study room / self-study room
• 図書館の自習室 = the library’s study room / the study room in the library

In English, we might translate this in several natural ways:

• the library study room
• the study room at the library
• the self-study room in the library

自習室 literally means a room for self-study.

• 自習 = self-study
• 室 = room

It often refers to a quiet place where people study on their own, rather than a classroom with a teacher. Depending on context, English translations could be:

• study room
• self-study room
• study area

で marks the place where an action happens.

Here, the action is 勉強しました (studied), and the place where it happened is 図書館の自習室.

So:

• 図書館の自習室で = in the library study room

A useful contrast:

• で = where an action happens
• に = where something exists, or the destination of movement, depending on the sentence

Because studying is an action, で is the correct particle here.

を marks the direct object of the verb, meaning the thing being acted on.

Here:

• 日本語 = Japanese language
• 日本語を勉強しました = studied Japanese

So 日本語 is what was studied, and を marks it as the object.

Japanese sentences typically place the verb at the end. This is one of the biggest word-order differences from English.

English:

• I studied Japanese in the library study room yesterday.

Japanese:

• Yesterday / in the library study room / Japanese / studied

So the sentence builds up information first, and the main action comes last.

Japanese often leaves out the subject when it is clear from context.

In this sentence, there is no explicit I, but it is understood from the situation. So the sentence naturally means something like:

• Yesterday, I studied Japanese in the library study room.

Japanese often omits:

• I
• you
• he/she
• other information that listeners can already infer

This is very normal and natural.

勉強しました is the polite past form.

• 勉強した = plain past
• 勉強しました = polite past

Both mean studied, but 勉強しました is more polite and is commonly used in:

• classroom Japanese
• everyday polite conversation
• speaking to people you are not close with

So this sentence is in polite style.

Grammatically, it is often analyzed as:

• 勉強 = study
• しました = did

So literally, 勉強しました is like did study. But as a whole, it functions as the verb studied.

Many Japanese verbs are made this way with する:

• 勉強する = to study
• 運動する = to exercise
• 旅行する = to travel

Then in polite past:

• 勉強しました
• 運動しました
• 旅行しました

Yes, Japanese word order is fairly flexible as long as the particles stay correct and the verb remains at the end.

For example, these are all possible:

• きのうは図書館の自習室で日本語を勉強しました。
• 図書館の自習室で、きのうは日本語を勉強しました。
• 日本語をきのうは図書館の自習室で勉強しました。

They all mean roughly the same thing, but the emphasis can change slightly depending on what comes earlier.

Still, the original order is very natural for learners and easy to understand.

You are right: normal Japanese writing usually does not use spaces between words.

So the sentence would normally be written like this:

きのうは図書館の自習室で日本語を勉強しました。

Spaces are often added in beginner materials to help learners see:

• where one word ends and another begins
• which particles attach to which words

So the spaced version is for learning convenience, not standard writing.

Yes. きのう is often written as:

• 昨日

So the full sentence could also be written:

昨日は図書館の自習室で日本語を勉強しました。

In beginner materials, hiragana is often used more often to make reading easier.