Després de la classe, tornaré a la biblioteca perquè vull llegir.

Després de means after.

In Catalan, després normally takes de before a noun or infinitive:

• després de la classe = after class / after the class
• després de dinar = after eating / after lunch

So de is part of the normal pattern, not an extra word.

La classe refers to a specific class, or to the class session the speaker has just had.

Catalan often uses the definite article a bit more than English does. Compare:

• després de la classe = after the class / after class, referring to a particular class
• després de classe = after class, more general or institutional in feel

In this sentence, la classe sounds very natural because it points to a concrete class period.

Tornaré is the future simple of tornar, in the first person singular:

• tornar = to return / to go back
• tornaré = I will return / I will go back

The ending -é shows I in the future.

It can do both, depending on the structure.

• tornar a + place = to return to a place

  • tornaré a la biblioteca = I will return to the library

• tornar a + infinitive = to do something again

  • tornaré a llegir = I will read again

So in your sentence, tornaré a la biblioteca clearly means I will go back to the library, not I will again the library or anything like that.

Because Catalan contracts a + el to al, but a + la stays a la.

So:

• a + el parc → al parc
• a + la biblioteca → a la biblioteca

Since biblioteca is feminine, you use la, and there is no contraction.

Catalan often leaves out subject pronouns because the verb ending already shows who the subject is.

• tornaré already means I will return
• vull already means I want

So jo is unnecessary unless you want emphasis or contrast:

• Jo tornaré, però ell no = I will return, but he will not

In a normal sentence, leaving out jo is the most natural choice.

Here perquè means because.

It introduces the reason:

• tornaré a la biblioteca perquè vull llegir
  = I will return to the library because I want to read

This is one of the most common uses of perquè in Catalan.

This is a very common confusion.

• perquè = because
• per què = why or for which

Examples:

• No hi vaig perquè estava cansat. = I did not go because I was tired.
• Per què hi vas? = Why did you go?

So in your sentence, the one-word form perquè is correct because it gives a reason.

After voler meaning to want, Catalan uses the infinitive directly:

• vull llegir = I want to read
• vols menjar = you want to eat
• volen sortir = they want to go out

So there is no extra preposition between vull and llegir.

Because the speaker’s desire exists now, and that present desire explains the future action.

So the logic is:

• After class, I will return to the library
• because I want to read

This mix is very natural in Catalan, just as it is in English. The future action is motivated by a present wish.

It is very natural and correct.

The phrase Després de la classe is a time expression placed at the beginning of the sentence, and Catalan often separates that kind of introductory phrase with a comma:

• Després de la classe, tornaré a la biblioteca...

In very short sentences, people may sometimes omit the comma, but using it here is good standard punctuation.

Yes. Catalan is fairly flexible with word order, especially with time expressions.

For example, you could also say:

• Tornaré a la biblioteca després de la classe perquè vull llegir.

That means the same thing. Starting with Després de la classe simply puts the time frame first.

They mainly show stress and, in many cases, the type of vowel.

• després → stress on the last syllable: des-PRÉS
• tornaré → stress on the last syllable: tor-na-RÉ
• perquè → stress on the last syllable: per-QUÈ

The accents also distinguish vowel quality:

• é is generally a closed e
• è is generally an open e

So the accents are not optional decoration; they are part of correct spelling and pronunciation.