Ni renkontiĝos ĉe la universitato post la prelego.

-os is the future tense ending in Esperanto. It means the action will happen in the future.

So:

• renkontiĝas = meet / are meeting
• renkontiĝis = met
• renkontiĝos = will meet

In this sentence, Ni renkontiĝos means we will meet.

This is a very common question.

• renkontos = will meet someone
• renkontiĝos = will meet with each other / will come together

In practice:

• Mi renkontos ŝin. = I will meet her.
• Ni renkontiĝos. = We will meet (each other).

So renkontiĝi often has a mutual sense: the people involved are meeting one another, not just one person meeting another person as an object.

The suffix -iĝ- often gives the idea of becoming, getting into a state, or sometimes an intransitive / non-object-taking version of a verb.

With renkontiĝi, it creates the idea of coming together or meeting one another, rather than meeting a direct object.

That is why:

• renkonti = to meet someone
• renkontiĝi = to meet, to meet each other, to come together

You do not need to translate -iĝ- literally every time. It is better to learn renkontiĝi as a normal word meaning to meet with each other.

ĉe usually means at, by, or at the place of.
en means in or inside.

So:

• ĉe la universitato = at the university
  This can mean at the university as a location, possibly outside it, near it, or on its grounds.
• en la universitato = in the university
  This sounds more specifically inside the university building/institution.

In many situations, Esperanto prefers ĉe when English would say at.

Because there is no direct object here, and the nouns are already introduced by prepositions.

In Esperanto, -n is mainly used for:

1. the direct object
2. sometimes direction after certain place expressions

Here we have:

• ĉe la universitato — introduced by the preposition ĉe
• post la prelego — introduced by the preposition post

After a preposition, nouns normally do not take -n.

So:

• ĉe la universitato is correct
• post la prelego is correct

Because post is a preposition, and prepositions normally take a noun without the accusative -n.

So the standard form is:

• post la prelego = after the lecture

You would only use -n in special cases, such as showing direction or when there is no preposition and the accusative is doing another job. That is not happening here.

la is the definite article, meaning the.

It is used here because the speaker has a specific university and a specific lecture in mind:

• la universitato = the university
• la prelego = the lecture

For English speakers, la universitato can feel slightly surprising, because English sometimes says at university or at college without the. Esperanto is usually more straightforward here and often uses la when a specific place or event is meant.

Yes, Esperanto word order is fairly flexible, as long as the sentence stays clear.

The original sentence:

• Ni renkontiĝos ĉe la universitato post la prelego.

You could also say:

• Post la prelego ni renkontiĝos ĉe la universitato.
• Ĉe la universitato ni renkontiĝos post la prelego.

These all mean basically the same thing, but the emphasis changes a little:

• putting post la prelego first emphasizes the time
• putting ĉe la universitato first emphasizes the place

The original order sounds natural and neutral.

Yes, in normal usage that is the natural meaning.

Because the verb is renkontiĝi, it already suggests a mutual meeting. So ni renkontiĝos is understood as we will meet in the sense that the members of the group are meeting one another.

If you said Ni renkontos..., listeners would usually expect a direct object after it, such as:

• Ni renkontos la profesoron. = We will meet the professor.

Esperanto stress is always on the second-to-last syllable.

Break renkontiĝos into syllables:

• ren-kon-ti-ĜOS

So the stress is on ĜOS? Wait — count carefully:

ren-kon-ti-ĝos has 4 syllables, so the stress is on the second-to-last one: ti.

So it is pronounced roughly:

• ren-kon-TI-ĝos

A rough English-style guide:

• ren like ren in rent without the final t
• kon like cone with a shorter vowel
• ti like tee
• ĝos with ĝ like the j in jam, so roughly jos

Also:

• ĝ is pronounced like English j in job
• ĉe is pronounced like cheh
• prelego is stressed on LE: pre-LE-go

post is a preposition meaning after.

It connects the time expression la prelego to the rest of the sentence:

• post la prelego = after the lecture

So it tells you when the meeting will happen.

Yes. That is also correct.

Both of these are natural:

• Ni renkontiĝos ĉe la universitato post la prelego.
• Ni renkontiĝos post la prelego ĉe la universitato.

The difference is mostly about flow and emphasis:

• ĉe la universitato post la prelego may feel like place first, then time
• post la prelego ĉe la universitato may feel like time first, then place

In ordinary conversation, either one works.