Després de treballar, la mare vol cuinar el dinar.

Because after després (after), Catalan commonly uses de + infinitive when the next idea is an action.

So:

• després de = after
• treballar = to work

Literally, després de treballar is after to work, but in natural English we say after working.

This is a very common pattern in Catalan:

• després de menjar = after eating
• després d'estudiar = after studying

English often uses -ing after prepositions; Catalan often uses the infinitive instead.

Formally, treballar is the infinitive, so it means to work.

But in this sentence, because it comes after després de, English translates it more naturally as working:

• després de treballar = after working

So the form is still the infinitive in Catalan, even though English uses a gerund.

The comma separates the introductory time phrase from the main clause:

• Després de treballar, = introductory phrase
• la mare vol cuinar el dinar = main clause

In English, this is similar to:

• After working, the mother wants to cook lunch.

In Catalan, this comma is natural and common when a phrase like this comes first, especially to make the sentence easier to read. In very short sentences it may sometimes be omitted, but here the comma sounds perfectly normal.

Catalan often uses the definite article with family members when talking about them:

• la mare = the mother / mum
• el pare = the father / dad

This is more natural in Catalan than leaving the noun bare.

So:

• La mare vol cuinar... = Mum/The mother wants to cook...

You would usually drop the article when directly addressing the person:

• Mare, vine! = Mum, come here!

Because Catalan often does not need a possessive where English might use one.

If it is already clear whose mother we mean, la mare is enough. In many contexts, la mare naturally means his mother, her mother, their mother, or simply mum, depending on the situation.

Using la seva mare is possible, but it is more explicit and only needed when you really want to specify ownership or avoid ambiguity.

Vol is the third person singular present of the verb voler (to want).

So:

• jo vull = I want
• tu vols = you want
• ell/ella vol = he/she wants

In this sentence:

• la mare vol = the mother wants

Because voler is followed directly by an infinitive in Catalan.

So you say:

• vol cuinar = wants to cook
• vol menjar = wants to eat
• vol sortir = wants to go out

No preposition is needed between vol and the infinitive.

This is similar to English want to + verb, except Catalan just uses the bare infinitive after voler.

Here dinar is being used as a noun, meaning lunch or the lunch meal.

The article el helps show that it is a noun:

• el dinar = the lunch / lunch

This is useful because dinar can also be a verb:

• dinar = to have lunch / to eat lunch

So cuinar el dinar clearly means to cook the lunch / to cook lunch, not to cook to have lunch.

In this context, the article sounds natural because we are talking about a specific meal being prepared.

It is correct and natural, but many speakers would also say fer el dinar.

The difference is roughly:

• cuinar el dinar = to cook lunch
  
  • focuses on the cooking itself
• fer el dinar = to make/prepare lunch
  
  • very common in everyday speech

So both are good, but fer el dinar may sound a bit more idiomatic in casual conversation.

Normally, it is understood to be the same person as the subject of the main clause unless context suggests otherwise.

So here the natural reading is:

• After working, the mother wants to cook lunch.

In other words, the mother is understood to be the one who worked.

Catalan often leaves this kind of subject unstated when it is clear from context.

Yes. Catalan word order is fairly flexible.

For example, you could also say:

• La mare vol cuinar el dinar després de treballar.

That still means The mother wants to cook lunch after working.

The original version puts the time phrase first:

• Després de treballar, la mare vol cuinar el dinar.

This gives a bit more emphasis to when the action happens.

The accent in després shows where the stress falls:

• després → stress on the last syllable

So it is pronounced roughly like des-PRES.

The accent also helps distinguish the vowel quality and shows that the word does not follow the default stress pattern. For learners, the main thing to remember is:

• després is stressed at the end, not at the beginning.