Mi ĝojas, ke vi venis.

Ke means that and introduces a subordinate clause.

So the sentence breaks down like this:

• Mi ĝojas = I am glad / I rejoice
• ke vi venis = that you came

In English, that is often optional: I’m glad (that) you came.
In Esperanto, ke is normally expressed when introducing this kind of clause.

Venis is the past tense of veni (to come).

Esperanto tense endings are very regular:

• -as = present
• -is = past
• -os = future

So:

• vi venas = you are coming / you come
• vi venis = you came
• vi venos = you will come

In Mi ĝojas, ke vi venis, the gladness is in the present, but the coming happened earlier. That is why the sentence uses:

• ĝojas = am glad now
• venis = came earlier

Because the speaker’s feeling is happening now.

Mi ĝojas means I am glad or I’m happy. The idea is: right now, I feel glad about the fact that you came.

This is very natural in Esperanto:

• present feeling/action in the main clause
• past event in the subordinate clause

So the timeline is:

1. you came
2. now I am glad about it

The base form is ĝoji, which means to rejoice, to be glad, or to feel joy.

From that root you get:

• ĝoji = to be glad
• ĝojas = am/is/are glad
• ĝojis = was/were glad
• ĝojos = will be glad

In everyday English, Mi ĝojas is often best translated as I’m glad rather than the more literal I rejoice.

Ĝ is pronounced like the j in jam or judge.

So ĝojas sounds approximately like:

• JO-yas

A rough breakdown:

• ĝo = like jo
• jas = like yas

Also remember:

• j by itself in Esperanto sounds like English y
• so the j in ĝojas is not a second English j sound

That is why ĝojas is not pronounced like jo-jas, but more like JO-yas.

Because Esperanto usually puts the tense directly on the main verb.

In English, you often say:

• I am glad

In Esperanto, ĝoji itself works as a verb:

• Mi ĝojas

So Esperanto does not need a separate am here.

However, Esperanto also allows an adjective-based version:

• Mi estas ĝoja, ke vi venis.

That also means I am glad that you came.

So both are possible:

• Mi ĝojas, ke vi venis.
• Mi estas ĝoja, ke vi venis.

The first is more verbal: I rejoice / I’m glad.
The second is more adjectival: I am glad.

Yes, it is correct.

Compare:

• Mi ĝojas, ke vi venis.
• Mi estas ĝoja, ke vi venis.

Both mean essentially I’m glad that you came.

The difference is mainly one of style and structure:

• Mi ĝojas uses the verb ĝoji
• Mi estas ĝoja uses the adjective ĝoja with estas

In many contexts, they are interchangeable.
Learners should recognize both, but Mi ĝojas is very common and natural.

Because there is no direct object here.

The accusative -n is usually used for:

1. a direct object
2. sometimes direction/motion toward something

In this sentence:

• Mi is the subject
• ĝojas is the verb
• ke vi venis is a subordinate clause, not a direct object noun
• vi is the subject of the subordinate clause

So no word needs -n.

Yes, to some extent.

The normal order is:

• Mi ĝojas, ke vi venis.

But Esperanto word order is fairly flexible, so you could also say:

• Ke vi venis, mi ĝojas.

That puts stronger emphasis on the fact that you came.

Still, the original order is the most neutral and most common for learners to use.

Vi can mean:

• you singular
• you plural

Esperanto uses the same pronoun for both.

So ke vi venis could mean:

• that you came (one person)
• that you came (more than one person)

The context tells you which is meant.

A very literal breakdown is:

• Mi = I
• ĝojas = rejoice / am glad
• ke = that
• vi = you
• venis = came

So literally:

I am glad that you came.

If you want to think of the structure, it is:

• main clause: Mi ĝojas
• subordinate clause: ke vi venis

That pattern is very common in Esperanto:

• Mi pensas, ke... = I think that...
• Mi scias, ke... = I know that...
• Mi esperas, ke... = I hope that...

So this sentence is also a useful model for many others.