
die Einladung
invitation
An oral or written request to take part in an event, visit someone, or be a guest.
Wir haben eine Einladung zur Hochzeit von Freunden erhalten.
We received an invitation to the wedding of some friends.
invitation
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invitation
An oral or written request to take part in an event, visit someone, or be a guest.
Wir haben eine Einladung zur Hochzeit von Freunden erhalten.
We received an invitation to the wedding of some friends.

invitation
Figuratively, a circumstance that provokes or encourages a certain, often negative, behavior.
Das offene Autofenster war eine reine Einladung zum Diebstahl.
The open car window was practically an invitation to theft.
'Die Einladung' (the invitation) is the noun related to the separable verb 'einladen' (to invite). The action is 'jemanden einladen' (to invite someone); the result or document is 'die Einladung' (the invitation).
Ich möchte dich zu meiner Party einladen.
I would like to invite you to my party.
To name the occasion for the invitation, German uses the preposition 'zu' followed by the dative. For example, 'die Einladung zum Geburtstag' (the invitation to the birthday party) or 'die Einladung zur Hochzeit' (the invitation to the wedding).
Danke für die Einladung zum Abendessen.
Thanks for the invitation to dinner.
Common verbs used together with 'Einladung' (invitation) are: 'eine Einladung bekommen' (to get an invitation), 'annehmen' (to accept), 'ablehnen' (to decline), 'aussprechen' (to extend), or 'verschicken' (to send out).
Leider muss ich deine Einladung ablehnen.
Unfortunately, I have to decline your invitation.
In the figurative meaning, 'Einladung' (invitation) describes a situation that practically invites negative behavior. This is not about a social event, but about an unwise action.
Die unverschlossene Tür war eine Einladung für Diebe.
The unlocked door was an invitation for thieves.
request / order
Both an Einladung and an Aufforderung can prompt someone to take an action. An Einladung emphasizes more of an opportunity that is open to be taken, while an Aufforderung directly calls for the action. Use „Einladung“ for an enticing circumstance, and „Aufforderung“ for a clear request or instruction.

Die offene Tür war für die Kinder eine Einladung, den Garten zu betreten.
The open door was an invitation for the children to enter the garden.
Das Schild „Bitte eintreten“ war für die Kinder eine Aufforderung, den Garten zu betreten.
The sign saying “Please enter” was a prompt for the children to enter the garden.