في الصباح أذهب إلى المكتبة قبل أن أذهب إلى الجامعة.

Arabic often puts a time expression at the beginning of the sentence to set the scene first. So في الصباح means in the morning, and placing it first is very natural.

The sentence could also be written with the verb first, but starting with the time phrase sounds smooth and common in MSA.

Literally, it means in the morning:

• في = in
• الصباح = the morning

So في الصباح is a standard way to say in the morning or during the morning.

A learner may also see صباحًا, which can also mean in the morning, but في الصباح is very clear and common.

Because the verb itself already shows the subject.

• أذهب = I go

The prefix أـ on the present-tense verb tells you the subject is I. So Arabic usually does not need the separate pronoun أنا unless you want emphasis or contrast.

For example:

• أذهب إلى المكتبة = I go to the library
• أنا أذهب إلى المكتبة = I go to the library / I am the one who goes to the library
  This sounds more emphatic.

أذهب is in the imperfect verb form. In Arabic, this form can express several things depending on context, including:

• present: I go / I am going
• habitual action: I go regularly
• future, in some contexts

In this sentence, because of في الصباح, it most naturally sounds like a habitual action:

• In the morning, I go to the library before I go to the university.

Because the standard MSA pattern is:

• ذهب إلى = to go to

So:

• أذهب إلى المكتبة = I go to the library
• أذهب إلى الجامعة = I go to the university

The preposition إلى shows the destination.

Because they mean the library and the university.

In Arabic, it is very common to use الـ when talking about a specific, known place. Even when English sometimes says go to school, go to university, or go to the library depending on context, Arabic often makes the noun definite if the place is understood or specific.

So here:

• المكتبة = the library
• الجامعة = the university

If you meant a library, you would usually say مكتبة without الـ.

Because the English idea before I go to the university is a full clause, and Arabic normally expresses that with another verb:

• قبل أن أذهب إلى الجامعة = before I go to the university

Repeating the verb is completely normal and natural in Arabic. Arabic does not usually shorten this in the same way English sometimes can.

Because قبل is followed here by a verb clause.

A very common MSA pattern is:

• قبل أن + present/imperfect verb

So:

• قبل أن أذهب = before I go

This is the normal way to say before when what follows is an action.

Compare:

• قبل أن أذهب إلى الجامعة = before I go to the university
• قبل الذهاب إلى الجامعة = before going to the university

The first uses a full clause; the second uses a verbal noun.

Yes. In MSA, أن makes the following imperfect verb subjunctive.

So if fully vowelled, you would have:

• أذهبُ in the main clause
• أن أذهبَ after أن

In normal Arabic writing, short vowels are usually not written, so both just appear as أذهب. But grammatically, the second one is in a different mood.

After a preposition in Arabic, the noun is normally in the genitive case.

So if fully vowelled, you would get:

• في الصباحِ
• إلى المكتبةِ
• إلى الجامعةِ

In everyday printed Arabic, these case endings are usually not written, but they are still part of the grammar.

Yes, very naturally.

Because the sentence includes في الصباح, it often sounds like a habit or usual routine:

• In the morning, I go to the library before I go to the university.

Without extra context, this is probably the most natural interpretation.

Yes. Both are possible, but they are structured differently.

• قبل أن أذهب إلى الجامعة = before I go to the university
• قبل الذهاب إلى الجامعة = before going to the university

The version with أن + verb sounds more like a full clause with an explicit subject, even though I is still built into the verb. The version with الذهاب uses the verbal noun going, which can sound slightly more formal or compressed.

Yes. In Modern Standard Arabic, the standard expression with ذهب is:

• ذهب إلى = went to
• يذهب إلى = goes to

Some spoken dialects may use other patterns, but in MSA, إلى الجامعة is the expected form.

Yes. Arabic word order is flexible.

For example, this is also grammatical:

• أذهب إلى المكتبة في الصباح قبل أن أذهب إلى الجامعة

But starting with في الصباح is often preferred when the speaker wants to foreground the time.

So the original sentence is not only correct; it is also very natural stylistically.