أمين المكتبة قرب استمارة العضوية.

Literally, أمين means something like keeper, custodian, or trusted person. In the phrase أمين المكتبة, it is joined to المكتبة in an iḍāfa construction, so the literal sense is the keeper/custodian of the library.

That is the normal Arabic way to express librarian in this kind of wording.

So:

• أمين = keeper, custodian
• المكتبة = the library
• أمين المكتبة = the librarian

Because أمين المكتبة is an iḍāfa phrase.

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun can make the whole phrase definite

So even though أمين by itself has no الـ, the whole phrase is definite because المكتبة is definite.

Compare the structure:

• أمين مكتبة = a librarian / a library keeper
• أمين المكتبة = the librarian / the keeper of the library

This is very common in Arabic.

It comes after أمين because Arabic expresses this relationship as an iḍāfa: X of Y.

So Arabic says:

• أمين المكتبة

where English would say:

• the librarian
• or more literally, the keeper of the library

Grammatically, المكتبة is the second term of the iḍāfa, so it is in the genitive case.

With full case endings, that part would be:

• أمينُ المكتبةِ

You usually do not see those endings written in normal Arabic text, but they are understood.

It is another iḍāfa.

Breakdown:

• استمارة = form
• العضوية = membership
• استمارة العضوية = membership form

Literally, it is the form of the membership, but in natural English we usually say membership form.

A useful thing to notice:

• the first noun, استمارة, does not take الـ
• the second noun, العضوية, does

That is normal for iḍāfa.

Because Arabic and English handle this structure differently.

In Arabic, when the second noun in an iḍāfa is definite, the whole phrase becomes definite. So استمارة العضوية is formally definite.

In English, though, we often do not show that definiteness so directly. We just say membership form, which can sound natural even when Arabic is using a definite structure.

So the Arabic is not strange here; it is just following Arabic rules for noun linkage.

Without vowel marks, قرب is ambiguous. It can represent different words.

The two most likely possibilities are:

• قَرَّبَ = he brought nearer / moved closer
• قُرْبَ = near or close to in an adverbial expression

So in unvowelled text, you often need context or the provided meaning to know which one is intended.

That means this written sentence could be read in more than one way unless the lesson or context tells you the meaning.

Because Arabic often omits the present-tense verb to be.

So if the sentence means The librarian is near the membership form, Arabic can simply say that without an explicit word for is.

This is very normal in Arabic nominal sentences.

So the structure would be understood as:

• أمين المكتبة = the librarian
• قرب استمارة العضوية = near the membership form

And English adds is, but Arabic does not need it in the present tense.

It would be something like:

• أمينُ المكتبةِ قُرْبَ استمارةِ العضويةِ

A rough pronunciation is:

• amīnu l-maktabati qurb(a) istimārati l-ʿuḍwiyyati

Here is what is happening:

• أمينُ is nominative
• المكتبةِ is genitive because of iḍāfa
• قُرْبَ is an adverbial expression meaning near
• استمارةِ is genitive after قرب
• العضويةِ is genitive as the second part of another iḍāfa

Then it would be:

• أمينُ المكتبةِ قَرَّبَ استمارةَ العضويةِ

A rough pronunciation is:

• amīnu l-maktabati qarraba istimārata l-ʿuḍwiyyati

In that reading:

• أمينُ المكتبةِ = the librarian
• قَرَّبَ = brought nearer / moved closer
• استمارةَ العضويةِ = the membership form

And grammatically:

• أمينُ is nominative
• المكتبةِ is genitive in iḍāfa
• استمارةَ is accusative as the direct object
• العضويةِ is genitive in iḍāfa

Usually from one of these things:

• the translation given in the lesson
• the wider context
• what makes sense semantically
• vowel marks, if they are provided

This is a very common feature of Arabic writing. Native readers also rely on context.

So if your lesson already gives the meaning, that meaning tells you whether to read قرب as:

• قُرْبَ = near
  or
• قَرَّبَ = brought nearer

That is not a problem with your Arabic; it is just how normal unvowelled Arabic script works.