Δεν έχω μάθημα σήμερα, άρα μπορώ να κάνω βόλτα στο πάρκο.

Greek often leaves out subject pronouns because the verb ending already shows who the subject is.

• έχω = I have
• μπορώ = I can

So Δεν έχω μάθημα σήμερα already clearly means I don’t have class today without needing εγώ.

You can add εγώ, but usually only for emphasis or contrast:

• Εγώ δεν έχω μάθημα σήμερα, αλλά ο αδερφός μου έχει.
  I don’t have class today, but my brother does.

δεν is the normal negation word used with indicative verbs in Modern Greek, and it goes directly before the verb:

• έχω = I have
• δεν έχω = I do not have

So:

• Δεν έχω μάθημα = I don’t have class

A useful contrast:

• δεν negates ordinary statements
• μη(ν) is used with subjunctive forms, commands, and some other structures

For example:

• Δεν πάω. = I’m not going.
• Να μην πάω; = Should I not go?

έχω μάθημα is a very common Greek expression meaning I have class / I have a lesson. It usually appears without an article when you mean class in a general schedule sense.

Compare:

• Έχω μάθημα σήμερα. = I have class today.
• Έχω ένα μάθημα σήμερα. = I have one class / one lesson today.
• Έχω το μάθημα σήμερα. = I have the class today.
  This sounds more specific, referring to a particular class already known from context.

So the version in your sentence is the natural general expression.

μάθημα can mean several related things depending on context:

• lesson
• class
• school subject

In Δεν έχω μάθημα σήμερα, it most naturally means class or lesson—something scheduled, such as a school or university session.

Examples:

• Το μάθημα αρχίζει στις οκτώ. = The class starts at eight.
• Τα μαθηματικά είναι το αγαπημένο μου μάθημα. = Math is my favorite subject.

άρα means therefore, so, thus, or as a result. It introduces a conclusion based on what was said before.

In this sentence:

• Δεν έχω μάθημα σήμερα, άρα μπορώ...
• I don’t have class today, so / therefore I can...

It is perfectly normal Greek. Depending on tone and style, Greek speakers might also use:

• οπότε = so, therefore
• λοιπόν = so, then
• έτσι = so, thus

άρα can sound a little more logical or inferential than casual οπότε, but it is still very common.

Modern Greek does not use the infinitive the way English does. Instead, after verbs like μπορώ (I can / I am able), Greek normally uses να + verb.

So:

• μπορώ να κάνω = I can do / I can take / I can go for

This is the standard pattern:

• Μπορώ να πάω. = I can go.
• Μπορώ να διαβάσω. = I can read / study.
• Μπορώ να κοιμηθώ. = I can sleep.

So if you’re looking for the English-style infinitive to do, Greek usually expresses that idea with να κάνω.

After να, Greek uses what learners often call the subjunctive or dependent verb form. For many verbs, this looks exactly like the present-tense form.

So in:

• να κάνω

the form κάνω looks like the ordinary present I do, but here it is functioning inside the να structure.

With μπορώ να κάνω, the sense is I can do / I can go for.

A very important point: Greek often distinguishes continuous and single/complete action after να.

Compare:

• μπορώ να κάνω βόλτα = I can go for a walk / be out walking
• μπορώ να πάω = I can go
• μπορώ να διαβάζω = I can be reading / read habitually
• μπορώ να διαβάσω = I can read / finish reading / read once

In your sentence, κάνω βόλτα is the normal idiomatic choice.

Yes, literally it is something like I do/take a walk, but you should learn κάνω βόλτα as a fixed expression.

It commonly means:

• go for a walk
• take a walk
• go for a stroll
• sometimes more broadly go out for a little outing

Examples:

• Κάνω βόλτα στο πάρκο. = I’m taking a walk in the park.
• Πάμε βόλτα; = Shall we go for a walk / go out?
• Βγήκα για βόλτα. = I went out for a walk.

So even though κάνω often means do/make, here the whole phrase has its own natural meaning.

στο is a contraction of:

• σε = in, at, to
• το = the

So:

• σε το πάρκο becomes στο πάρκο

This contraction is standard and extremely common.

Other examples:

• σε τη(ν) πόλη → usually στην πόλη
• σε τον φίλο → στον φίλο
• σε ένα σπίτι stays σε ένα σπίτι because there is no definite article to contract with

πάρκο here is in the accusative case, because the preposition σε normally takes the accusative in Modern Greek.

So:

• στο πάρκο = in/at/to the park

For this noun, πάρκο, the nominative and accusative singular happen to look the same:

• nominative: το πάρκο
• accusative: το πάρκο

That is why the form doesn’t visibly change.

With a masculine noun, the case change is easier to see:

• nominative: ο φίλος
• accusative: τον φίλο
• στον φίλο = to the friend

Because they are being used differently.

• έχω μάθημα is a fixed, general expression meaning I have class
• στο πάρκο refers to a specific location, the park

So Greek treats them differently:

• μάθημα = general activity/schedule item, no article
• το πάρκο = definite place, so article is natural

This is similar to how English sometimes drops articles in set expressions:

• go to school
• be in class
• but go to the park

Yes. Greek word order is fairly flexible, and moving σήμερα changes emphasis more than basic meaning.

Your sentence:

• Δεν έχω μάθημα σήμερα, άρα μπορώ να κάνω βόλτα στο πάρκο.

Other natural possibilities:

• Σήμερα δεν έχω μάθημα, άρα μπορώ να κάνω βόλτα στο πάρκο.
• Δεν έχω σήμερα μάθημα...
  This is possible, though often a bit less neutral in everyday speech.

In general:

• putting σήμερα first gives it more emphasis
• keeping it after μάθημα sounds very natural and neutral here

It is very natural and usually preferred, because άρα introduces a conclusion and links two clauses.

So:

• Δεν έχω μάθημα σήμερα, άρα μπορώ να κάνω βόλτα στο πάρκο.

The comma helps show the logical break:

1. I don’t have class today
2. therefore, I can take a walk in the park

In informal writing, punctuation can be looser, but the comma here is standard and helpful.

A natural pronunciation would keep the stress on the written accent marks:

• Δεν É-ho MÁ-thi-ma SÍ-me-ra, Á-ra bo-RÓ na KÁ-no VÓL-ta sto PÁR-ko.

A few useful notes:

• δεν έχω is usually said smoothly together
• στο is unstressed and clings to πάρκο
• βόλτα has the stress on the first syllable: VÓL-ta
• μπορώ has stress on the last syllable: bo-RÓ

If spoken naturally, the voice will usually rise a little before the comma and then continue smoothly after άρα.