Expressing "to leave" with partir/laisser/quitter/sortir in French

In French, depending on context you will use one of these four verbs to express to leavepartirlaisserquitter  or sortir.

Look at these sentences:

Je suis parti tôt ce soir.I left early tonight.

Vous êtes sortis de la pièce avant nous.You came out of the room before us.  
(You left the room before us.)

Je quitte cette ville pour de bon.I'm leaving this town for good.

Nous avons laissé les passeports dans la voiture !We left the passports in the car!

Note the following distinctions:

Partir

- partir means to leave / to go away. You can use it on its own (e.g. I leave = Je pars).
When used with a place, it will always be followed by a preposition (e.g. I leave from / for  = Je pars de / pour)
Je pars de cette ville.I'm leaving this town.

Elle part tous les jours à six heures.She leaves every day at six.

Special case: 
It's very colloquial to say partir en vacances for to go on holiday:

Cette année, nous partons en vacances en hiver.This year, we're going (away) on holiday in the winter.

Sortir

sortir means to go/come out.
When used with de, as in sortir de + place, it can express the idea of leaving [somewhere], i.e. going/coming out of a place.
Je sors de la maison.I'm going out of the house.  
(I'm leaving the house.)

Nous sortons juste du métro.We're just coming out of the metro.
(We're just leaving the metro.)

Quitter

- quitter means to leave some place / somewhere. You cannot use it on its own: it always needs an object, and it can be used for places and people (i.e. to break up).
Il a quitté son travail.He quit his job.

Elle quitte Patrick pour quelqu'un d'autre.She's leaving Patrick for someone else.

Quitter is also the only one to mean to leave / quit a job or [someone] for good.

Laisser

- laisser means to leave something / to let. You cannot use it on its own. However, this one is NOT used for places, only to leave people or things in places.
Je laisse ma fille à l'école.I'm leaving my daughter at school.

Tu laisses la porte ouverte tous les soirs.You leave the door open every evening.

J'ai laissé mon chien chez ma mère pour le weekend.I left my dog at my mother's house for the weekend.

 

Grammar Jargon:   
partir 
is an intransitive verb, whereas quitter and laisser are always transitive verbs (i.e. have a direct object) and sortir can be either.

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Examples and resources

Nous sortons juste du métro.We're just coming out of the metro.
(We're just leaving the metro.)
Tu laisses la porte ouverte tous les soirs.You leave the door open every evening.
Je sors de la maison.I'm going out of the house.  
(I'm leaving the house.)
Il a quitté son travail.He quit his job.
J'ai laissé mon chien chez ma mère pour le weekend.I left my dog at my mother's house for the weekend.
Nous avons laissé les passeports dans la voiture !We left the passports in the car!
Je laisse ma fille à l'école.I'm leaving my daughter at school.
Elle quitte Patrick pour quelqu'un d'autre.She's leaving Patrick for someone else.
Je quitte cette ville pour de bon.I'm leaving this town for good.
Nous allons partir de Paris.We are going to leave from Paris.
Je pars de cette ville.I'm leaving this town.
Cette année, nous partons en vacances en hiver.This year, we're going (away) on holiday in the winter.
Elle part tous les jours à six heures.She leaves every day at six.
Je vais laisser mes clés sur la table.I'm going to leave my keys on the table.
Je suis parti tôt ce soir.I left early tonight.
Vous êtes sortis de la pièce avant nous.You came out of the room before us.  
(You left the room before us.)
I'll be right with you...