في كل اسبوع اذهب الى المكتبة مرة واحدة.

The version you saw is the same sentence written without short vowels and case endings, which is very common in everyday Arabic writing.

A fully vocalized version is:

في كلِّ أسبوعٍ أذهبُ إلى المكتبةِ مرّةً واحدةً.

Those extra marks show:

• short vowels
• case endings
• the correct hamza spelling in words like أسبوع and إلى

In normal printed Arabic, learners often see:

• أسبوع instead of اسبوع
• إلى instead of الى

So your sentence is understandable as written, but the more standard spelling is:

في كل أسبوع أذهب إلى المكتبة مرة واحدة.

في كل أسبوع is a time expression meaning every week or literally in every week.

Arabic often places time expressions at the beginning of a sentence. This is very natural. So:

• في كل أسبوع أذهب إلى المكتبة مرة واحدة
• أذهب إلى المكتبة مرة واحدة في كل أسبوع

Both are possible.

Starting with في كل أسبوع gives a slight emphasis to the time frame: every week, I go to the library once.

كل means every or all, depending on context.

In this sentence, كل أسبوع means every week.

A useful pattern is:

• كل يوم = every day
• كل أسبوع = every week
• كل شهر = every month
• كل سنة = every year

So كل is a very common word for repeated time expressions.

After كل, Arabic usually uses a noun in the singular, and it is often indefinite when the meaning is every ....

So:

• كل أسبوع = every week

If you say:

• كل الأسبوع

that usually means something more like the whole week or all week, not every week.

So the indefinite أسبوع is correct for the meaning here.

المكتبة means the library.

In many cases, Arabic uses the definite article الـ where English might say the, or where the specific place is understood from context. If you are talking about the library as a known place, المكتبة is natural.

• إلى المكتبة = to the library
• إلى مكتبة = to a library

So if the meaning is a regular, familiar destination, المكتبة makes sense.

Because ذهب / يذهب often takes إلى to show movement to a place.

So:

• أذهب إلى المدرسة = I go to school
• أذهب إلى البيت = I go home / to the house
• أذهب إلى المكتبة = I go to the library

This is similar to English go to.

أذهب is the present/future tense, first person singular, from the verb ذهب (to go).

It means:

• I go
• I am going
• sometimes I will go, depending on context

Here, because the sentence describes a habit, أذهب means I go.

Some related forms:

• أذهب = I go
• تذهب = you go / she goes
• يذهب = he goes
• نذهب = we go

Arabic often expresses once as مرّةً واحدةً, literally one time.

• مرّة = time / occasion
• واحدة = one (feminine)

Since مرّة is a feminine noun, the number one agrees with it and becomes واحدة, not واحد.

So:

• مرة واحدة = once
• مرتين = twice
• ثلاث مرات = three times

This is a very common pattern in Arabic.

Because مرّة is feminine.

In Arabic, adjectives and numbers used like adjectives must agree with the noun in gender. Since مرّة is feminine, one must also be feminine:

• مرّة واحدة = one time / once

Compare:

• كتاب واحد = one book
• سيارة واحدة = one car

So واحدة matches the feminine noun مرّة.

In fully vocalized Arabic, the sentence would be:

في كلِّ أسبوعٍ أذهبُ إلى المكتبةِ مرّةً واحدةً.

Here is what is happening:

• في is a preposition, so the noun after it is genitive:
  • أسبوعٍ
• كلِّ is also in the genitive here because it comes after في
• إلى is a preposition, so:
  • المكتبةِ is genitive
• أذهبُ ends in ـُ because it is indicative
• مرّةً واحدةً is in the accusative because it functions as an adverbial expression of number/frequency

If you are still a beginner, you do not need to produce all these endings in ordinary writing, but it is useful to know why they exist.

Because كل comes after the preposition في.

Prepositions in Arabic normally put the following word into the genitive case. Since كل is the first word after في, it becomes:

• في كلِّ

Then the noun after كل is also genitive:

• أسبوعٍ

So the full phrase is:

• في كلِّ أسبوعٍ

Yes. That is also correct and very common.

• كل أسبوع أذهب إلى المكتبة مرة واحدة
• في كل أسبوع أذهب إلى المكتبة مرة واحدة

Both mean essentially the same thing.

Using في makes the phrase a little more explicitly in every week, while omitting it often sounds slightly simpler and very natural.

It is one of the most common and straightforward ways, especially in clear standard Arabic.

Examples:

• ذهبت مرة واحدة = I went once
• أزورهم مرة واحدة في الشهر = I visit them once a month

Arabic also has other ways to express frequency depending on style, but مرة واحدة is standard, simple, and widely understood.

A careful pronunciation would be close to:

fī kulli usbūʿin adhhabu ilā al-maktabati marratan wāḥidatan

A few notes:

• أسبوع is pronounced roughly usbūʿ
• أذهب begins with a hamza sound: adhhabu
• إلى is ilā
• مرّة has a doubled r sound
• واحدة contains ḥ, a stronger breathy h sound than English h

In normal speech, many final case endings are weakened or dropped, but in formal reading they are part of the full pronunciation.