בספרייה יש גם צעירים וגם מבוגרים, וכל האנשים שם קוראים בשקט.

בספרייה is made from:

• ב־ = in
• ספרייה = library

When ב־ is added to a noun with ה־ (the), Hebrew usually merges them into one form. So:

• ב + הספרייה → בספרייה

So בספרייה means in the library, not just in a library.

יש is the Hebrew existential word meaning there is or there are.

So:

• בספרייה יש... = In the library there is/there are...

A very important point: יש does not change for singular or plural.

• יש ילד = there is a boy
• יש ילדים = there are children

In your sentence, even though there are plural people, Hebrew still uses the same יש.

גם ... וגם means both ... and ...

So:

• גם צעירים וגם מבוגרים = both young people and adults / older people

This is a very common pattern in Hebrew.

Examples:

• גם קפה וגם תה = both coffee and tea
• גם בנים וגם בנות = both boys and girls

The ו at the start of the second וגם is just and.

They are originally adjectives, but here they are being used like nouns.

• צעיר = young
• מבוגר = adult / older / grown-up

In this sentence:

• צעירים = young people
• מבוגרים = adults / older people

Hebrew does this a lot. English does it too sometimes, as in the rich, the poor, the young.

If the speaker wanted to be more explicit, they could say:

• אנשים צעירים ואנשים מבוגרים = young people and adult/older people

But that sounds less natural here.

Not exactly.

מבוגר / מבוגרים usually means adult / adults, or sometimes older people in contrast to children or youth. It does not automatically mean elderly.

So in this sentence, the contrast is:

• צעירים = young people
• מבוגרים = adults / older people

If you specifically wanted elderly people, Hebrew would usually use another word, such as זקנים depending on context.

Because the sentence is doing two different things.

In the first clause:

• יש גם צעירים וגם מבוגרים
  = there are both young people and adults

These are being introduced as general groups, so they are indefinite.

In the second clause:

• וכל האנשים שם...
  = and all the people there...

Now the speaker is referring to the whole set of people already present in that place, so Hebrew uses a definite noun:

• האנשים = the people

Also, with כל:

• כל האנשים = all the people

This is normal Hebrew structure.

אנשים means people, and it is the common plural form associated with איש (man/person).

It is not a simple regular plural like adding ־ים to the singular in the usual way learners expect. So it is worth memorizing as a vocabulary item:

• איש = man / person
• אנשים = people

In modern Hebrew, אנשים is very common and often just means people in general.

קוראים is the masculine plural present-tense form of to read.

It matches האנשים:

• האיש קורא = the man/person reads
• האנשים קוראים = the people read

In Hebrew, present-tense verbs agree with the subject in gender and number.

Here, אנשים takes masculine plural agreement, so:

• קוראים is correct

If the subject were an all-female group, you would expect:

• קוראות

Also, Hebrew present tense can mean both:

• read
• are reading

So קוראים here can naturally mean read or are reading, depending on context.

You're right: forms from the root ק־ר־א can relate to both reading and calling.

So קוראים can mean:

• read / are reading
• call / are calling
• sometimes are called in other constructions

Context tells you which meaning is intended.

Here, because the sentence talks about a library and adds בשקט (quietly / in silence), the meaning is clearly:

• קוראים = reading

שם means there.

So:

• כל האנשים שם = all the people there

It refers back to the place already mentioned, the library.

Hebrew often uses שם this way to mean there / in that place.

Hebrew often expresses adverbs with a preposition + noun phrase.

בשקט literally comes from:

• ב־ = in
• שקט = quiet / silence

Together, בשקט means:

• quietly
• in silence
• softly, depending on context

So:

• קוראים בשקט = read quietly / are reading in silence

This is a very natural Hebrew expression.

The sentence has two parts:

1. בספרייה יש גם צעירים וגם מבוגרים
   = In the library, there are both young people and adults.

2. וכל האנשים שם קוראים בשקט
   = And all the people there are reading quietly.

A literal breakdown is:

• בספרייה = in the library
• יש = there are
• גם צעירים וגם מבוגרים = both young people and adults
• וכל = and all
• האנשים = the people
• שם = there
• קוראים = read / are reading
• בשקט = quietly / in silence

So the Hebrew is very natural, even if the word-for-word order is a little different from English.