
vortragen
to present
To present, recite, or perform something in front of an audience, for example a poem, a song, or a report.
Jeder Student musste im Seminar ein Referat vortragen.
Every student had to present a paper in the seminar.
to present / put forward
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to present
To present, recite, or perform something in front of an audience, for example a poem, a song, or a report.
Jeder Student musste im Seminar ein Referat vortragen.
Every student had to present a paper in the seminar.

to put forward
To formally express or put forward a concern, request, or complaint.
Der Bürger trug sein Anliegen persönlich beim Bürgermeister vor.
The citizen put forward his concern to the mayor in person.

to carry forward
To physically carry something forward. This meaning is rare and often formal or literary.
Der Page musste die Krone auf einem Samtkissen vortragen.
The page had to carry the crown forward on a velvet cushion.
'Vortragen' (to present / put forward) is a separable verb with the prefix 'vor-'. In a main clause, the prefix stands at the end; in a subordinate clause, the verb stays together; and in the infinitive, 'zu' stands between 'vor' and 'tragen'.
Der Schüler trug sein Gedicht selbstbewusst vor.
The student confidently recited his poem.
The verb consists of 'vor' (in the sense of 'forward' or 'in front of others') and 'tragen' (to carry). This structure helps you understand the meanings: you 'carry' something verbally before an audience, or you bring a concern 'before' a person.
Er hat seine Argumente sehr überzeugend vorgetragen.
He presented his arguments very convincingly.
In the meaning 'to present', 'vortragen' is often combined with artistic or academic content. Typical phrases are: 'ein Gedicht vortragen' (to recite a poem), 'ein Lied vortragen' (to perform a song), 'ein Referat vortragen' (to give a presentation), or 'eine Geschichte vortragen' (to tell/perform a story).
Die Band wird heute Abend ihre neuen Lieder vortragen.
The band will perform their new songs this evening.
When you 'vorträgt' (put forward) a concern or request, this usually happens in a formal or official context, for example at a government office, with a supervisor, or in court.
Die Anwältin trug die Argumente ihrer Mandantin vor Gericht vor.
The lawyer put forward her client's arguments in court.
The literal meaning 'to carry something forward' is very rare today. It is used almost only in literary, historical, or very ceremonial contexts.
Bei der Zeremonie wurde die Fahne feierlich vorgetragen.
At the ceremony, the flag was solemnly carried forward.
to hold
You can both halten and vortragen a speech. „Eine Rede halten“ refers more to the public appearance as a whole, while „vortragen“ places more emphasis on presenting the prepared content. halten usually fits the appearance, while vortragen also fits presenting a prepared text.

Die Bürgermeisterin trug bei der Feier ihre sorgfältig vorbereitete Rede vor.
The mayor presented her carefully prepared speech at the celebration.
Die Bürgermeisterin hielt bei der Feier eine Rede vor dem ganzen Publikum.
The mayor gave a speech in front of the entire audience at the celebration.