
aufführen
to perform
To present a play, a piece of music, or a dance before an audience.
Die Theater-AG wird nächstes Wochenende „Faust“ aufführen.
The school theater group will perform 'Faust' next weekend.
to perform / to list
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to perform
To present a play, a piece of music, or a dance before an audience.
Die Theater-AG wird nächstes Wochenende „Faust“ aufführen.
The school theater group will perform 'Faust' next weekend.

to list
To name or record individual points, names, or items in a list.
Bitte führen Sie in der Abrechnung alle entstandenen Kosten einzeln auf.
Please list all costs incurred individually in the expense statement.

to behave
To behave in a particular, often conspicuous or inappropriate way.
Benimm dich und führ dich nicht auf wie ein kleines Kind!
Behave yourself and don't act like a little child!
'Aufführen' (to perform/to list) is a separable verb. The prefix 'auf' appears at the end of the main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Die Kinder führen ein kleines Theaterstück auf.
The children are performing a short play.
You can recognize the meaning of 'aufführen' (to perform/to list) from the object or the grammar. If it is about art (theater, music), it means 'darbieten' (to present/perform). If it is about information (costs, names), it means 'auflisten' (to list). If the verb is reflexive ('sich aufführen'), it is about behavior.
Das Orchester führt eine Symphonie von Mozart auf.
The orchestra is performing a symphony by Mozart.
In the meaning 'darbieten' (to present/perform), 'aufführen' (to perform) is typically combined with artistic works. Common objects are: a play, an opera, a musical, a dance, or a concert.
Die Ballettschule führt jedes Jahr den „Nussknacker“ auf.
The ballet school performs 'The Nutcracker' every year.
In the meaning 'sich verhalten' (to behave), 'aufführen' is always reflexive. The reflexive pronoun ('sich') must be adapted to the subject of the sentence (ich führe mich auf, du führst dich auf).
Warum führst du dich so seltsam auf?
Why are you behaving so strangely?
The phrase 'sich aufführen' (to behave/act up) almost always has a negative connotation. It describes behavior that is perceived as inappropriate, childish, strange, or embarrassing.
Hör auf, dich so aufzuführen, die Leute schauen schon!
Stop acting like that; people are already looking!
to play
Both words can refer to a performance before an audience or in a film. „Spielen“ refers especially to a person's role or to a person's playing music. „Aufführen“ focuses more strongly on the entire play, piece of music, or dance as a work being performed. Depending on the focus, either word can therefore be appropriate.

Das Theater führt das neue Stück im Herbst vor Publikum auf.
The theater will perform the new play for an audience in the fall.
Die Schauspielerin spielt die Hauptrolle in dem neuen Film.
The actress plays the leading role in the new film.