zyugyou no ato, tosyokan ni yotte hukusyuusimasu.

Because あと is a noun. It means after or the time after.

In Japanese, one noun often connects to another with の, so 授業のあと is literally something like the after of class, which naturally becomes after class in English.

You can see the same pattern in:

• 食事のあと = after the meal
• 仕事のあと = after work

So の is not showing possession here. It is linking two nouns.

Here, に goes with 寄る.

With 寄る, the particle に marks the place you stop by:

• コンビニに寄る = stop by the convenience store
• 駅に寄る = stop by the station

So 図書館に寄って means stopping by the library.

A very common point of confusion is に versus で:

• 図書館に寄る = stop by the library
• 図書館で復習する = review at the library

In this sentence, に belongs to 寄って, not to 復習します.

寄る means to stop by, drop in, or go via somewhere.

It usually suggests that the place is not the only or main destination, but a place you visit on the way or as an extra stop. So it has a lighter nuance than simply saying 行く.

Compare:

• 図書館に行きます = I go to the library
• 図書館に寄ります = I stop by the library

So 寄る gives the feeling of making a brief or incidental stop.

寄る is a godan verb ending in る. For this type of verb, the て-form changes る to って.

So:

• 寄る → 寄って

This is the same pattern as:

• 帰る → 帰って
• 取る → 取って

This is different from ichidan verbs, where る becomes て:

• 食べる → 食べて
• 見る → 見て

So 寄って is the regular て-form of 寄る.

The て-form is being used to connect two actions in one sentence.

So:

• 図書館に寄って復習します

means:

• stop by the library, and then review

In this kind of sentence, the first action usually happens before the second one.

Also, in polite Japanese, only the last verb usually carries ます, so you do not say 寄ります復習します. Instead, you connect the first verb with the て-form:

• 寄って、復習します

The final verb 復習します carries the tense and politeness for the sentence.

Not completely explicitly, but that is the most natural interpretation.

Grammatically, 図書館に directly goes with 寄って, so the sentence literally says that the speaker stops by the library and then reviews. In normal context, people will usually understand that the review happens there.

If you want to make the location of the review more explicit, you could say:

• 図書館で復習します = review at the library
• 図書館に寄って、そこで復習します = stop by the library and review there

So the original sentence relies on natural context rather than spelling everything out.

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

In English, you usually need to say I, he, they, and so on. In Japanese, that information is often omitted if the listener can understand it.

So this sentence does not need 私は unless the speaker wants to emphasize the topic or create contrast.

For example:

• 私は授業のあと、図書館に寄って復習します。

is possible, but it is not necessary in many situations.

復習する is a very common noun + する verb, and it works naturally as 復習します.

So:

• 復習します = review, do review

This is often the most natural way to say it.

復習をします is also possible, but it can sound a little more formal, deliberate, or heavier depending on context. In everyday textbook-style Japanese, 復習します is usually the simpler and more natural choice.

If you want to say exactly what is being reviewed, you can add an object:

• 今日習ったことを復習します
• ノートを復習します

No. The spaces are usually just there to help learners read the sentence.

In normal Japanese writing, it would be written like this:

授業のあと、図書館に寄って復習します。

Japanese normally does not put spaces between words the way English does.