فهرس المكتبة قرب قاعة القراءة.

Because Arabic usually omits the present-tense verb “to be”.

So instead of saying something like The library catalog is near the reading hall, Arabic simply puts:

• the thing being talked about: فهرس المكتبة
• then the information about its location: قرب قاعة القراءة

This is called a nominal sentence in Arabic. In grammar terms:

• فهرس المكتبة = the subject
• قرب قاعة القراءة = the predicate, giving location

If you wanted a past or future meaning, then Arabic would use an actual verb.

Because فهرس المكتبة is an iḍāfa construction, often called a construct phrase.

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun shows whether the whole phrase is definite or indefinite

So:

• فهرس مكتبة = a library catalog or catalog of a library
• فهرس المكتبة = the library’s catalog / the library catalog

Even without الـ on فهرس, the whole phrase is definite because المكتبة is definite.

Yes. That is exactly how the structure works.

Arabic often expresses possession or close relationships by putting two nouns together:

• فهرس = catalog / index
• المكتبة = the library

So فهرس المكتبة literally means catalog of the library, which is natural English as the library catalog.

This is one of the most common patterns in Arabic, and English speakers need to get used to it because Arabic uses it very often instead of of or apostrophe-s.

For the same reason: it is also an iḍāfa.

• قاعة = hall
• القراءة = the reading

So literally it is hall of reading, which English expresses as reading hall or reading room/hall, depending on context.

Again, the first noun in the iḍāfa usually does not take الـ, even when the whole phrase is definite. So قاعة القراءة can still mean the reading hall.

It is often translated like a preposition, but grammatically it is better thought of as a noun/adverbial expression meaning “nearness” or “near”.

In this sentence, قرب introduces location:

• قرب قاعة القراءة = near the reading hall

A useful way to understand it is:

• قرب is functioning like an adverbial noun
• the phrase after it is linked to it in an iḍāfa-like relationship

That is why Arabic can say:

• قرب قاعة القراءة

instead of needing:

• من

By contrast, if you use قريب, the adjective near, then you normally say:

• فهرس المكتبة قريب من قاعة القراءة

So both are possible, but the structure changes:

• قرب + noun
• قريب من + noun

A fully vocalized version would be:

فِهْرِسُ الْمَكْتَبَةِ قُرْبَ قَاعَةِ الْقِرَاءَةِ

Here is why:

• فِهْرِسُ: nominative, because it is the subject of the nominal sentence
• الْمَكْتَبَةِ: genitive, because it is the second term of the iḍāfa
• قُرْبَ: accusative, because it is being used adverbially as a ظرف
• قَاعَةِ: genitive, because it is connected to قرب
• الْقِرَاءَةِ: genitive, because it is the second term of قاعة القراءة

In normal Arabic writing, these short vowels are usually omitted, so learners have to infer them from grammar and context.

It is a complete sentence.

It may look short to an English speaker, but in Arabic it is fully complete:

• فهرس المكتبة = what we are talking about
• قرب قاعة القراءة = where it is

So it has the same structure as other simple Arabic nominal sentences, such as:

• الكتاب على الطاولة = The book is on the table
• المدرسة أمام المسجد = The school is in front of the mosque

No extra verb is needed in the present tense.

Yes. That is a very natural alternative.

Compare the two:

• فهرس المكتبة قرب قاعة القراءة
• فهرس المكتبة قريب من قاعة القراءة

Both mean essentially the same thing. The difference is mainly structural:

• قرب = a location expression meaning near
• قريب من = adjective + preposition, literally near to

The first version is compact and very common in formal written Arabic. The second may feel a bit more transparent to learners because it looks more like an English-style predicate.

A careful MSA pronunciation with case endings is roughly:

fihrisu al-maktabati qurba qāʿati al-qirāʾati

In ordinary pause-style reading, many final short vowels are dropped, so you may hear something closer to:

fihris al-maktaba qurb qāʿat al-qirāʾa

A few pronunciation notes:

• فهرس = fihris
• قاعة contains ع, a deep throat consonant
• قراءة contains a hamza: qirāʾa

If you are still early in Arabic, the most important thing is to recognize the structure and stress pattern; perfect pronunciation of ع and ء usually takes time.