densya wo matte iru aida, tetyou wo yomikaesimasu.

Because the sentence contains two different verbs, and each verb has its own object:

• 電車を待っている = waiting for the train
• 手帳を読み返します = reread the notebook/planner

So the structure is basically:

• [電車を待っているあいだ], = while waiting for the train
• [手帳を読み返します] = I reread my planner

Each を belongs to a different verb, so this is completely normal.

In Japanese, 待つ usually takes a direct object with を.

So:

• 電車を待つ = wait for the train
• 友だちを待つ = wait for a friend

This is different from English, where wait often needs for. A natural way to think about it is:

• English: wait for X
• Japanese: X を 待つ

So 電車を待っている is exactly what you would expect in Japanese.

待っている is the て-form of 待つ plus いる.

• 待つ = to wait
• 待っている = be waiting

Here it shows an ongoing action/state. The speaker is in the middle of waiting.

So:

• 電車を待つ = to wait for the train
• 電車を待っている = to be waiting for the train

In this sentence, that ongoing action becomes the time period for the main action: while being in the state of waiting for the train, I reread my planner.

あいだ means while, during, or for the time that.

In this sentence:

• 電車を待っているあいだ = while I am waiting for the train

The clause before あいだ describes the time span, and the main clause tells you what happens during that time.

So the pattern is:

• [verb / clause] + あいだ = while doing..., during the time when...

Examples:

• 日本にいるあいだ = while I am in Japan
• ご飯を食べているあいだ = while eating

This is a very common question.

A simple way to understand it:

• あいだ = throughout that time / during that period
• あいだに = at some point within that time

So:

• 電車を待っているあいだ、手帳を読み返します。
  This suggests the rereading happens as something you do during the waiting time.

• 電車を待っているあいだに、手帳を読み返します。
  This sounds more like at some point while waiting, I reread it.

The difference is often subtle, and in real life both may be possible depending on nuance. But as a rule of thumb:

• あいだ = focus on the whole span
• あいだに = focus on an event happening within that span

Because in Japanese, subordinate parts of a sentence often use the plain form, even when the main sentence ends politely.

Here:

• 電車を待っているあいだ = subordinate time clause
• 手帳を読み返します = main clause

It is very normal to say:

• 待っているあいだ、読み返します。

rather than:

• 待っていますあいだ、読み返します。 ← unnatural

So this is not inconsistent. It is standard Japanese grammar:

• plain form inside the clause before あいだ
• polite form at the end of the full sentence

読み返します comes from 読み返す, which means:

• read again
• look back over
• reread

It is a compound verb:

• 読む = to read
• 返す = to return / do again / back

So 読み返す gives the idea of going back and reading something again.

That means:

• 手帳を読みます = I read my planner/notebook
• 手帳を読み返します = I reread / look back through my planner/notebook

So the sentence is not just about reading, but about reviewing something already written there.

Japanese non-past forms can cover several meanings that English separates.

• 待っている here is present progressive: am waiting
• 読み返します is non-past polite, which can mean:
  • I reread
  • I will reread
  • I reread habitually / usually

Without more context, the sentence could mean:

• something the speaker usually does while waiting for the train, or
• something the speaker will do in a particular situation

So Japanese often leaves this a bit broader than English does.

The subject is omitted, which is extremely common in Japanese.

From context, a natural interpretation is I:

• While waiting for the train, I reread my planner.

But Japanese does not have to say 私は if it is already understood.

Depending on context, it could also theoretically be:

• he
• she
• we
• another understood person

In isolation, English usually chooses I because it sounds most natural.

Japanese often puts time expressions and background information before the main action.

So this order is very natural:

• 電車を待っているあいだ、手帳を読み返します。

It works like:

• As for the time while I’m waiting for the train, I reread my planner.

Also, Japanese verbs usually come at the end of their clause, so:

• 電車を待っている ends with the verb for that clause
• 手帳を読み返します ends with the main verb of the whole sentence

That is why the sentence order feels different from English.

No, normal Japanese is usually written without spaces.

The standard way to write this sentence is:

電車を待っているあいだ、手帳を読み返します。

The spaces in your example are probably there only to help learners see the parts more clearly.

So the spaced version is a teaching aid, not the usual style of native writing.