
lassen
to let
To allow or permit someone to do something.
Meine Eltern lassen mich am Wochenende mit Freunden ausgehen.
My parents let me go out with friends on the weekend.
to let / to have
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to let
To allow or permit someone to do something.
Meine Eltern lassen mich am Wochenende mit Freunden ausgehen.
My parents let me go out with friends on the weekend.

to have done
To arrange for something to be done by another person. You do not do it yourself.
Ich muss meine Haare schneiden lassen.
I have to have my hair cut.

to leave
To leave something behind in a place or not take it with you.
Ich habe meinen Regenschirm im Büro gelassen.
I left my umbrella at the office.

to stop
To stop doing something; to refrain from an action. Often used as a command.
Lass das, du machst alles kaputt!
Stop that, you're breaking everything!

to be possible
In combination with an infinitive, it expresses possibility, similar to a passive construction with 'können' (can).
Die Tür lässt sich nicht öffnen.
The door cannot be opened.

to leave
To leave something in a particular state or not change it.
Lass das Fenster bitte offen, es ist so warm hier drin.
Please leave the window open; it is so warm in here.

to leave someone alone
A fixed expression meaning not to disturb or bother someone.
Bitte lass mich in Ruhe, ich muss mich konzentrieren.
Please leave me alone; I need to concentrate.
In many of its meanings, 'lassen' is used like a modal verb and appears with a second verb in the infinitive. This second verb always comes at the end of the sentence or clause.
Ich lasse mein Fahrrad in der Werkstatt reparieren.
I am having my bicycle repaired at the workshop.
When 'lassen' is used with a second verb in the perfect tense, a special form is created: 'haben' + infinitive + infinitive of 'lassen'. This construction is called 'Ersatzinfinitiv' (substitute infinitive) or 'doppelter Infinitiv' (double infinitive).
Sie hat mich eine Stunde warten lassen.
She made me wait for an hour.
The context determines whether 'lassen' means 'erlauben' (to allow) or 'veranlassen' (to arrange / to have something done). If it is about a person's wish, it often means 'to allow.' If it is about a paid service, it means 'to arrange / to have something done.'
Der Lehrer lässt die Schüler im Unterricht diskutieren.
The teacher lets the students discuss in class.
In the meaning 'zurücklassen' (to leave behind) or 'nicht mitnehmen' (not to take along), 'lassen' stands alone, without a second verb in the infinitive. The perfect tense is formed regularly here with 'hat gelassen'.
Oh nein, ich habe mein Handy im Auto gelassen!
Oh no, I left my phone in the car!
The construction 'sich lassen' + infinitive is a common alternative to the passive with 'können' (can). It expresses that something is possible or can be done.
Der Fleck lässt sich nicht entfernen.
The stain cannot be removed.
The meaning 'veranlassen' (to arrange / to have something done) is very often used for services that you do not perform yourself. Typical examples are 'sich die Haare schneiden lassen' (to have one's hair cut) or 'das Auto waschen lassen' (to have the car washed).
Alle zwei Jahre lasse ich meine Augen vom Arzt kontrollieren.
Every two years I have my eyes checked by the doctor.
In the imperative, 'Lass das!' (Stop that!) or 'Lass das sein!' (Stop doing that!) is used as a clear command to stop a particular action immediately.
Lass das, der Hund hat Angst vor dir!
Stop that, the dog is afraid of you!
to leave / to entrust
Lassen can express leaving something unchanged in a particular state, such as leaving an exit open. Überlassen occurs in the fixed expression etwas dem Zufall überlassen and means deliberately not planning or controlling something. In this expression, Zufall takes the dative.

Wir lassen den Ausgang des Abends offen und machen keinen festen Plan.
We’re leaving the outcome of the evening open and aren’t making a firm plan.
Wir überlassen den Ausgang des Abends dem Zufall und machen keinen festen Plan.
We’re leaving the outcome of the evening to chance and aren’t making a firm plan.