erlauben
to allow
To give someone permission or approval to do something; to permit something.
Meine Eltern erlauben mir, am Wochenende länger aufzubleiben.
My parents allow me to stay up later on the weekend.

to allow
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to allow
To give someone permission or approval to do something; to permit something.
Meine Eltern erlauben mir, am Wochenende länger aufzubleiben.
My parents allow me to stay up later on the weekend.

'Erlauben' (to allow) is an inseparable verb. The prefix 'er-' remains firmly attached to the verb stem in all tenses and sentence constructions.
Er erlaubt seinem Sohn, mit Freunden ins Kino zu gehen.
He allows his son to go to the movies with friends.
The word family includes 'die Erlaubnis' (permission) and 'der Urlaub' (vacation). 'Urlaub' originally meant permission to leave work or duty.
Ohne die Erlaubnis der Eltern darfst du nicht mitfahren.
Without the parents' permission, you're not allowed to come along.
When you permit someone to do something, the person receiving the permission is always in the dative. The construction is either 'jemandem etwas erlauben' (to allow someone something) or 'jemandem erlauben, etwas zu tun' (to allow someone to do something).
Ich erlaube dir die Nutzung meines Computers.
I allow you to use my computer.
In the meaning 'sich etwas leisten' (to afford something), the verb is reflexive. The person is the subject and the reflexive pronoun is in the dative: 'Ich erlaube mir einen teuren Urlaub.' (I allow myself an expensive vacation.)
Diesen Luxus kann ich mir leider nicht erlauben.
Unfortunately, I can't afford this luxury.
The expression 'Was erlauben Sie sich?' is a fixed phrase used to express outrage at rude behavior. The verb is used reflexively here.
Einfach vorzudrängeln! Was erlauben Sie sich eigentlich?
Just pushing ahead like that! What gives you the right?
to let / to have
'lassen' and 'erlauben' can both mean that someone is allowed to do something. 'lassen' often sounds more everyday and is used especially in simple situations involving people. 'erlauben' sounds a bit more precise or official, for example with rules, parents, teachers, or authorities. In many sentences, you can use both, but 'erlauben' emphasizes the permission more strongly.

Die Lehrerin erlaubt den Schülern, im Unterricht ein Wörterbuch zu benutzen.
The teacher allows the students to use a dictionary in class.
Meine Eltern lassen mich heute Abend länger draußen bleiben.
My parents let me stay out later this evening.