Learn Hardcore Greek: Αν τελειώσω νωρίς, θα σε πάρω τηλέφωνο.

Yes. Αν means if and introduces a condition. In this sentence it sets up the condition Αν τελειώσω νωρίς (If I finish early), followed by the result θα σε πάρω τηλέφωνο (I’ll call you).

What form is τελειώσω? Why isn’t it τελειώνω?

τελειώσω is the aorist subjunctive (1st person singular) of τελειώνω/τελειώνω (I finish / I’m finishing).
After Αν (when talking about a real future possibility), Greek typically uses the subjunctive form, not the present indicative.

Αν τελειώσω = if I finish (at some point, once) → completion-focused
Αν τελειώνω would sound wrong here (it’s indicative and doesn’t fit this conditional pattern)

Why is there no word meaning I? How do we know who is finishing?

Greek commonly drops subject pronouns because the verb ending shows the person.
τελειώσω ends in -ω, which here marks 1st person singular (I). You can add εγώ (I) for emphasis, but it’s usually unnecessary:

Αν (εγώ) τελειώσω νωρίς…

What exactly does νωρίς modify, and can it move around?

νωρίς means early and here modifies τελειώσω (finish early). It’s flexible in position:

Αν τελειώσω νωρίς, … (most natural)
Αν νωρίς τελειώσω, … (possible but more marked/emphatic)
Θα σε πάρω τηλέφωνο αν τελειώσω νωρίς. (also very common)

Why do we need θα? What does it do?

θα is the particle that forms the future (and some other modal meanings). It corresponds to will / I’m going to depending on context.
So θα σε πάρω = I will call you.

Why is it θα σε πάρω and not θα παίρνω?

Because Greek distinguishes aspect in the future:

θα σε πάρω (τηλέφωνο) = I’ll call you (once / at a specific moment) → aorist (single completed action)
θα σε παίρνω (τηλέφωνο) = I’ll be calling you / I’ll call you repeatedly → imperfective (habitual/repeated/ongoing)

In this context (a single call after finishing), θα σε πάρω is the natural choice.

What is σε exactly, and why is it before the verb?

σε is the weak object pronoun meaning you (singular, informal). It’s placed before the verb in standard word order:

θα σε πάρω = I will call you

If you wanted formal/plural you, you’d use σας:

θα σας πάρω τηλέφωνο

Is σε ever optional here?

Only if the object (you) is already clear from context, but normally you keep it because πάρω τηλέφωνο alone can mean I’ll make a call (not necessarily to you).
So θα σε πάρω τηλέφωνο is the clear, standard way to say I’ll call you.

Why does Greek say πάρω τηλέφωνο (literally take phone) for call?

παίρνω τηλέφωνο is a very common idiom meaning to phone / to call (someone).
Greek also has the verb τηλεφωνώ (I call/phone), which is slightly more formal or neutral:

Αν τελειώσω νωρίς, θα σου τηλεφωνήσω. (also correct)

But θα σε πάρω τηλέφωνο is extremely everyday and natural.

Why is it τηλέφωνο without a preposition, like on the phone or by phone?

In Greek, τηλέφωνο in this expression acts like the thing you “take/do”: παίρνω τηλέφωνο = make a phone call. No preposition is needed.
If you wanted to say by phone as a method, you might use other phrasing, but for I’ll call you, the idiom is the normal choice.

Do we always need the comma after νωρίς?

It’s standard to use a comma when the if-clause comes first:

Αν τελειώσω νωρίς, θα σε πάρω τηλέφωνο.

If you reverse the order, the comma is often omitted:

Θα σε πάρω τηλέφωνο αν τελειώσω νωρίς.

How should I pronounce Αν τελειώσω—does the ν change before τ?

In fast, natural speech, the final ν of Αν may be lightly pronounced or assimilated before a t sound, so it can sound like it’s blending into the next word. You’ll commonly hear something close to:

Αντελειώσω… (smoothly connected)

But in careful speech you can still pronounce the ν clearly; both are fine.