Learn Hardcore Greek: Μου αρέσει να ταξιδεύω με το αεροπλάνο.

So the Greek structure is “To me is pleasing [something]”, not “I like [something]”.
English: subject = I.
Greek: grammatical subject is what pleases you, and μου just marks to whom it is pleasing.

Why is it μου and not εγώ for “I”?

εγώ is the subject pronoun I (nominative case).
In Μου αρέσει, “I” is not the grammatical subject; the subject is the thing that pleases you.

Greek uses the genitive case to show to whom something is pleasing:

μου – to me
σου – to you (singular)
του / της – to him / to her
μας – to us
σας – to you (plural/formal)
τους – to them

So:

Μου αρέσει… = It is pleasing to me.
Σου αρέσει… = It is pleasing to you.

Why is αρέσει in the third person singular?

Because the subject of the verb is not “I”, but the thing you like.

In Μου αρέσει να ταξιδεύω με το αεροπλάνο:

Subject = the whole clause να ταξιδεύω με το αεροπλάνο (to travel by plane).
That clause counts as a singular thing, so the verb αρέσει is in 3rd person singular.

You will also see:

Μου αρέσει το βιβλίο. – I like the book.
Μου αρέσουν τα βιβλία. – I like the books.

Here the verb agrees in number with what is liked (το βιβλίο singular → αρέσει; τα βιβλία plural → αρέσουν).

What is the role of να in να ταξιδεύω?

να is a particle that introduces a verb in a non‑finite way, often called the subjunctive in Greek.

Here, να ταξιδεύω corresponds roughly to English “to travel” or “traveling” in a general sense.

Some common uses of να:

After verbs of liking/wanting:
- Μου αρέσει να ταξιδεύω. – I like to travel.
- Θέλω να ταξιδέψω. – I want to travel (on a specific occasion).
After πρέπει (must), μπορώ (can), etc.:
- Πρέπει να φύγω. – I must leave.

So in this sentence, να just introduces the action that is pleasing to you.

Why is it ταξιδεύω and not ταξιδέψω?

Greek has two main aspects for verbs in the subjunctive/να form:

Imperfective (ongoing / repeated / habitual): ταξιδεύω
→ used for general likes, habits, repeated actions
Perfective (single, complete event): ταξιδέψω
→ used for one specific trip / one occurrence

In Μου αρέσει να ταξιδεύω με το αεροπλάνο, you are talking about a general preference (in general, I like traveling by plane), so the imperfective ταξιδεύω is correct.

If you said:

Θέλω να ταξιδέψω με το αεροπλάνο.
→ I want to (go and) travel by plane (on a specific trip).

What does με mean here? Is it “with” or “by”?

Basic meaning of με is with, but in Greek it is also used where English uses by for means of transport.

So:

με το αεροπλάνο = with the airplane → functionally by plane
με το λεωφορείο = by bus
με το τρένο = by train
με τα πόδια = on foot

So Μου αρέσει να ταξιδεύω με το αεροπλάνο. = I like to travel by plane.

Why is it το αεροπλάνο with the article το? In English we just say “by plane”.

Greek uses the definite article much more often than English.

With means of transport, the usual pattern is:

με το αεροπλάνο – by plane
με το τρένο – by train
με το λεωφορείο – by bus

Even though English drops the article, Greek normally keeps it.
Saying με αεροπλάνο (without το) is possible but sounds more formal or less natural in everyday speech.

So, for everyday Greek, prefer the form με το + [transport].

Could I say Μου αρέσουν τα αεροπλάνα instead? What’s the difference?

Yes, but the meaning changes slightly.

Μου αρέσει να ταξιδεύω με το αεροπλάνο.
→ I like traveling by plane (the activity).
Μου αρέσουν τα αεροπλάνα.
→ I like airplanes (as objects – you like planes themselves, maybe their design, the idea of planes, etc.).

So the first sentence focuses on the action of traveling, the second on the things (planes).

How would I say “I don’t like to travel by plane”?

Just add δεν in front of μου αρέσει:

Δεν μου αρέσει να ταξιδεύω με το αεροπλάνο.
= I don’t like to travel by plane.

Word order is:

Δεν
- (clitic pronoun) + αρέσει
  → Δεν μου αρέσει …

Can the word order change? For example, can I put μου somewhere else?

The most natural order is exactly as in the sentence:

Μου αρέσει να ταξιδεύω με το αεροπλάνο.

Because μου is an unstressed clitic, it usually comes right before the verb αρέσει.

You might see variations for emphasis, but many of them sound unnatural or too marked in everyday speech. For a learner, it is safest to keep:

[Pronoun in genitive] + αρέσει + [thing you like]

Examples:

Σου αρέσει να ταξιδεύεις με το αεροπλάνο; – Do you like to travel by plane?
Του αρέσει να ταξιδεύει με το αεροπλάνο. – He likes to travel by plane.

How do I say “He/She/We/They like to travel by plane”?

You keep αρέσει (since the subject is still the general action “to travel”) and you change only the genitive pronoun:

Του αρέσει να ταξιδεύει με το αεροπλάνο. – He likes to travel by plane.
Της αρέσει να ταξιδεύει με το αεροπλάνο. – She likes to travel by plane.
Μας αρέσει να ταξιδεύουμε με το αεροπλάνο. – We like to travel by plane.
Σας αρέσει να ταξιδεύετε με το αεροπλάνο. – You (plural/formal) like to travel by plane.
Τους αρέσει να ταξιδεύουν με το αεροπλάνο. – They like to travel by plane.

Note that the inner verb (ταξιδεύω) also changes to match each person (ταξιδεύω, ταξιδεύεις, ταξιδεύει, ταξιδεύουμε, ταξιδεύετε, ταξιδεύουν).

Is να ταξιδεύω more like English “to travel” or “traveling”?

It can correspond to either, depending on context. Greek να + verb doesn’t match perfectly with one English form.

In this specific sentence:

Μου αρέσει να ταξιδεύω με το αεροπλάνο.

You could translate equally well as:

I like to travel by plane.
I like traveling by plane.

Both express a general preference, which is exactly what the Greek sentence means.