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
Loading your saved state.
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.

'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
'eine Rede halten' and 'vortragen' both have to do with speaking in front of other people. 'eine Rede halten' fits especially when someone gives an address to an audience, for example at a celebration, a meeting, or an event. 'vortragen' is broader: you can present or recite a text, a poem, a song, or a report. Learners may confuse the words because in both cases someone is speaking in front of others. As a guide: you give a speech ('eine Rede halten'), but you present or recite a prepared text or contribution ('vortragen').

Morgen trägt mein Bruder in der Schule ein Gedicht vor.
Tomorrow my brother is reciting a poem at school.
Lisa hält bei der Feier eine kurze Rede für ihre Eltern.
Lisa gives a short speech for her parents at the celebration.