der Eingang
entrance
An area through which one can enter a building, room, or site.
Der Eingang des Museums befindet sich auf der rechten Seite.
The entrance to the museum is on the right-hand side.

entrance / receipt
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entrance
An area through which one can enter a building, room, or site.
Der Eingang des Museums befindet sich auf der rechten Seite.
The entrance to the museum is on the right-hand side.

The word 'Eingang' (entrance / receipt) is made up of the prefix 'ein-' and the noun 'Gang' (from 'gehen' (to go)). So it literally describes a 'way in' to a building or area.
Bitte benutzen Sie den Eingang auf der Rückseite des Gebäudes.
Please use the entrance at the back of the building.
You can recognize the meaning of 'Eingang' (entrance / receipt) from the context. If it is about a place (house, museum), it means access or entrance. If it is about mail or data (letter, email, payment), it means arrival or receipt. With works (book, music), it means the beginning.
Der Eingang zum Park ist bis 20 Uhr geöffnet.
The entrance to the park is open until 8 p.m.
To describe a location, use 'am Eingang' (at the entrance). To express movement toward it, say 'zum Eingang' (to the entrance).
Wir treffen uns in zehn Minuten am Haupteingang.
We'll meet in ten minutes at the main entrance.
In the meaning 'Eintreffen' (arrival/receipt), 'Eingang' (receipt) is used mainly in formal written language, in the office, or in business correspondence.
Nach Eingang der Zahlung versenden wir die Ware umgehend.
After receipt of payment, we will ship the goods immediately.
Common combinations are 'den Eingang bestätigen' (to confirm receipt), 'nach Eingang' (after receipt), and 'bei Eingang' (upon receipt). A very common compound is 'der Posteingang' (inbox).
Bitte bestätigen Sie den Eingang dieser E-Mail kurz.
Please briefly confirm receipt of this email.
beginning
'der Anfang' and 'der Eingang' can both have to do with the first part of something. However, 'der Anfang' is the normal word for the beginning of a period of time, a text, a path, or a story. 'der Eingang' usually means the place through which you enter a building or room. Only with texts, music, or speeches can 'der Eingang' also mean the beginning; this sounds rather formal or technical. Learners may confuse the words because an entrance is often spatially at the beginning of a place. In practice: for a beginning, you usually say 'Anfang'; for a door or access point, 'Eingang'.

Meine Kollegin wartet am Eingang, weil sie die Tür nicht findet.
My colleague is waiting at the entrance because she cannot find the door.
Den Anfang des Films habe ich leider verpasst.
Unfortunately, I missed the beginning of the film.