Permitir vs. dejar
Both 'permitir' and 'dejar' can mean 'to let' or 'to allow', but they are used in different contexts and with different nuances in Spanish.
Permitir
The word 'permitir' means 'to permit' or 'to allow'. This verb is more formal and is often used in contexts where rules, regulations, or official permissions are involved.
El jefe permitió que tomáramos un descanso.
(The boss allowed us to take a break.)
No se permite fumar en el edificio.
(Smoking is not allowed in the building.)
Sus padres no le permiten salir hasta tarde.
(Her parents don't allow her to stay out late.)
El sistema no permite acceso sin contraseña.
(The system does not allow access without a password.)
Dejar
'Dejar' can also mean 'to let' or 'to allow', but it is less formal and more commonly used in everyday conversation. It can also mean 'to leave' or 'to stop doing something', adding to its versatility.
Déjame ayudarte con eso.
(Let me help you with that.)
Mi madre no me deja volver tarde a casa.
(My mother doesn't let me come home late.)
Voy a dejar mi trabajo a fin de mes.
(I'm going to leave my job at the end of the month.)
Dejó de fumar hace años.
(He stopped smoking years ago.)
Summary
'Permitir' is more formal and often used in official or regulated contexts, while 'dejar' is less formal and more common in everyday speech. Additionally, 'dejar' has other meanings like 'to leave' or 'to stop doing something', making it a more versatile word.