Learn Hardcore Greek: Για εμένα ο σκοπός είναι να περνάμε καλά μαζί στην τάξη. - For me the purpose is for us to have a good time together in class.

You will also very often hear Για μένα (shorter, more colloquial).
Both Για εμένα and Για μένα are correct; εμένα just sounds a bit more formal/emphatic than μένα.

Could we say Ο σκοπός για εμένα είναι… instead of Για εμένα ο σκοπός είναι…? Is there a difference?

Yes, you can say both:

Για εμένα ο σκοπός είναι…
Ο σκοπός για εμένα είναι…

The meaning is the same. The difference is emphasis and style:

Starting with Για εμένα puts more emphasis on “for me / in my view”.
Starting with Ο σκοπός sounds a bit more neutral, like you’re first defining the purpose and then adding “for me” as a comment.

Greek word order is quite flexible; changes mostly affect emphasis, not basic meaning.

What exactly does σκοπός mean here? Is it the same as στόχος or λόγος?

σκοπός roughly means purpose or aim.

Comparison:

σκοπός = purpose / aim (more general “what something is for”)
- Ο σκοπός είναι να περνάμε καλά. – The purpose is that we have a good time.
στόχος = target / goal (often more concrete, like a goal you try to reach)
- Στόχος του μαθήματος είναι να μάθουμε 10 λέξεις.
λόγος = reason / cause
- Ο λόγος που είμαι εδώ είναι… – The reason I am here is…

In your sentence, σκοπός fits best: the teacher is talking about the purpose of the class.

Why do we say είναι να περνάμε…? In English we use an infinitive: “the purpose is to have fun”.

Modern Greek does not use an infinitive like English “to have”. Instead, it uses:

να + verb (subjunctive form)

So:

English: The purpose is to have a good time.
Greek: Ο σκοπός είναι να περνάμε καλά.

Here να περνάμε functions like an infinitive clause: “to have (a good time)”. This να + verb structure is the normal way to express what in English would often be an infinitive.

What tense/mood is περνάμε in να περνάμε? Why not να περάσουμε?

Formally, after να, the verb is in the subjunctive mood. The forms of the present subjunctive look the same as the present indicative:

(εμείς) περνάμε = we pass / we spend time / we are having a good time

In να περνάμε, we have present subjunctive, which here expresses a general, ongoing situation:

να περνάμε καλά – that we (in general, regularly) have a good time

If you said:

να περάσουμε καλά (aorist subjunctive) – that we have a good time (on one particular occasion)

So να περνάμε καλά matches the idea of the general purpose of the class, not just one lesson.

Who does περνάμε refer to? Why first person plural (we) and not περνάτε (you) or περνάω (I)?

περνάμε is 1st person plural = we.

In context (a teacher talking), we means:

teacher + students together

So να περνάμε καλά μαζί στην τάξη = for us to have a good time together in class (all of us, not just the students or just the teacher).

να περνάτε καλά – that you (plural) have a good time
να περνάω καλά – that I have a good time

The choice of περνάμε highlights that the fun is shared by everyone present.

What does the expression περνάω καλά mean exactly? Is it literally “to pass well”?

Literally, περνάω can mean to pass, to spend (time), etc.
The idiomatic expression περνάω καλά means:

to have a good time / to enjoy oneself

Examples:

Πέρασα πολύ καλά χτες. – I had a great time yesterday.
Θέλω να περνάτε καλά στο μάθημα. – I want you to enjoy yourselves in class.

So in your sentence:

να περνάμε καλά = for us to have a good time / to enjoy ourselves

Why do we need μαζί (“together”) if περνάμε already means “we”? Isn’t it redundant?

μαζί = together.

Even though περνάμε (“we”) already suggests a group, μαζί adds a specific nuance:

It emphasizes that we are not just all in the same room, but sharing the experience, doing things together.
It makes the sentence warmer and more collaborative.

Without μαζί:

να περνάμε καλά στην τάξη – for us to have a good time in class

With μαζί:

να περνάμε καλά μαζί στην τάξη – for us to have a good time together in class (cooperative, joint experience)

It’s not grammatically necessary, but stylistically nice and clear.

What is στην in στην τάξη? Why not σε την τάξη or στη τάξη?

στην is a contraction:

σε (in/at) + την (the, feminine accusative) → στην

So:

σε την τάξη (theoretically)
becomes
στην τάξη – the correct, natural form

General pattern:

σε + την → στην
σε + τη → στη (before consonants)
σε + το → στο
σε + τον → στον

So στην τάξη = in the class / in the classroom.

Is there any difference between Για εμένα and Για μένα at the start of the sentence?

Both mean the same: for me / as far as I’m concerned.

Για εμένα – a bit more formal, careful, or emphatic
Για μένα – very common in everyday speech, slightly more casual

In spoken Greek you’ll probably hear Για μένα ο σκοπός είναι… more often, but both are correct and natural.