صندوق إعادة الكتب قرب الباب.

In Arabic, present-tense to be is usually omitted in simple statements.

So Arabic says:

صندوق إعادة الكتب قرب الباب

where English would say:

The book-return box is near the door.

This is called a nominal sentence.
If you wanted was, you would normally use كان:

كان صندوق إعادة الكتب قرب الباب = The book-return box was near the door.

Because صندوق إعادة الكتب is an iḍāfa construction, often called a construct phrase.

In an iḍāfa:

• the first noun is the مضاف
• the second noun is the مضاف إليه

The first noun normally does not take الـ.

So:

• صندوق = box
• إعادة الكتب = return of the books / book return

Together:

صندوق إعادة الكتب = the book-return box / book-return box

The whole phrase can be definite because definiteness is determined by the end of the iḍāfa chain, and here الكتب is definite.

It is a nested iḍāfa.

You can break it down like this:

1. إعادة الكتب = returning the books / book return
2. صندوق إعادة الكتب = box of book return

So the structure is basically:

[صندوق] [إعادة الكتب]

Arabic often uses noun-to-noun structures like this where English prefers compound nouns such as:

• book-return box
• return box
• book drop

إعادة is a verbal noun (maṣdar), from the verb أعاد = to return / to put back / to restore.

Arabic very often uses verbal nouns in labels, signs, and short descriptive phrases.

So instead of a full clause like:

box for returning books

Arabic naturally says something closer to:

box of returning-books

using the maṣdar:

إعادة = returning / return

This is very common in Modern Standard Arabic.

It is plural because the idea is general: this is a box for returning books, not one specific book.

It is definite (الكتب) because it is part of the iḍāfa chain, and that helps make the whole phrase definite.

Also, after a verbal noun like إعادة, the thing being returned can appear after it in an iḍāfa-style relationship:

• إعادة الكتب = returning the books / book return

If you used the singular الكتاب, it would suggest the book, meaning one specific book, which would change the sense.

Because إعادة ends in ة (tāʾ marbūṭa).

When a word ending in ة is said by itself or at a pause, it usually sounds like -a or -ah:

• إعادة = iʿāda

But when it is followed directly by another word in an iḍāfa construction, the ة is pronounced as t:

• إعادة الكتب = iʿādat al-kutub

So in this sentence, if you read it fully, you pronounce that t.

قرب here means near, but grammatically it is often treated as a noun used adverbially, a locative expression.

So:

• قرب الباب = near the door

The noun after it, الباب, is in the genitive.

A very common alternative expression is:

بالقرب من الباب = near the door

So both are possible, but قرب الباب is shorter and very natural.

Because قرب itself already carries the sense of nearness and directly links to the following noun.

So Arabic can simply say:

• قرب الباب = near the door

You do not need an extra word like من here.

That said, Arabic also allows the longer phrasing:

• بالقرب من الباب

Both mean essentially the same thing.

A fully vowelled version is:

صُنْدُوقُ إِعَادَةِ الْكُتُبِ قُرْبَ الْبَابِ

Here is what the endings show:

• صُنْدُوقُ — nominative, because it is the subject/topic
• إِعَادَةِ — genitive, because it is in iḍāfa after صندوق
• الْكُتُبِ — genitive, because it is in iḍāfa after إعادة
• قُرْبَ — accusative as an adverbial/locative expression
• الْبَابِ — genitive after قرب

In normal unvowelled writing, these case endings are not shown.

Yes, that is close to the Arabic structure, but it is not the most natural English.

A more literal breakdown is:

• صندوق = box
• إعادة الكتب = returning the books / book return

So literally it is something like:

box of book return

But natural English would usually say:

• book-return box
• book drop
• book return bin

So the Arabic structure is normal Arabic, even if the most natural English translation uses a different kind of phrasing.