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.

'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.
cargo / charge / summons
'die Einladung' and 'die Ladung' can both be a request to come somewhere. But the difference is important. An 'Einladung' is usually friendly or private: you are supposed to come to a celebration, a meal, or a visit. A 'Ladung' is official and comes, for example, from a court or an authority. It is not simply a nice request. Learners may confuse the words because of their similar form. In everyday life with friends, you almost always say 'Einladung'; for courts or authorities, you say 'Ladung'.

Für die Hochzeit hat Maria eine schöne Einladung an ihre Familie geschickt.
For the wedding, Maria sent a beautiful invitation to her family.
Wegen des Unfalls bekam der Fahrer eine Ladung vor Gericht.
Because of the accident, the driver received a summons to appear in court.