Learn Hardcore Greek: Την άλλη εβδομάδα δεν έχουμε μάθημα ελληνικών.

Την άλλη εβδομάδα is in the accusative case, because time expressions like “next week” are often put in the accusative in Greek when they answer “when?” (time when something happens).

εβδομάδα = week (feminine noun)
Feminine accusative singular takes the article την
So: η άλλη εβδομάδα (nominative – “the other/next week” as subject)
But: την άλλη εβδομάδα (accusative – “next week” as a time expression)

You can think of it roughly as “(during) next week we don’t have Greek class,” and that “during” is understood, so Greek uses the accusative.

What exactly does άλλη mean here? Is it literally “other week” or “next week”? What about επόμενη εβδομάδα?

Literally, άλλη means “other”.

However, in time expressions, Την άλλη εβδομάδα is the standard, everyday way to say “next week” in spoken Greek.

Την άλλη εβδομάδα = next week (very common, colloquial and neutral)
Την επόμενη εβδομάδα = the next week / the following week (a bit more formal or “bookish”, but also correct)

In most everyday contexts, άλλη and επόμενη here mean the same thing for “next week”, but άλλη is more idiomatic in speech.

Why isn’t there a word for “on” as in “on next week”? Why is it just Την άλλη εβδομάδα?

English often uses “on” with days and dates: on Monday, on the 5th.

Greek generally does not use a preposition here. Instead, it uses a bare time expression, often in the accusative:

Την άλλη εβδομάδα – (on) next week
Τη Δευτέρα – (on) Monday
Τον Μάιο – (in) May

So Την άλλη εβδομάδα by itself already means “(on) next week”, and adding a preposition like σε would be wrong in this case.

Why is the negative δεν placed before έχουμε? Could it ever go after the verb?

In standard Greek, the negative particle δεν (or δε in speech) always goes directly before the verb it negates.

Δεν έχουμε μάθημα. = We don’t have a class.
Δεν πηγαίνω. = I’m not going / I don’t go.

So δεν έχουμε is the only normal order.
Έχουμε δεν μάθημα… is incorrect in modern Greek.

Why is έχουμε (present tense) used if the meaning is about the future (“next week we don’t have…”)? Shouldn’t it be δεν θα έχουμε?

Greek often uses the present tense for fixed future arrangements, especially for timetables, schedules, and planned events:

Αύριο δεν έχουμε σχολείο. – Tomorrow we don’t have school.
Το βράδυ βγαίνω με φίλους. – This evening I’m going out with friends.

So:

Την άλλη εβδομάδα δεν έχουμε μάθημα ελληνικών.
= Next week we don’t have Greek class. (scheduled fact)

You can also say:

Την άλλη εβδομάδα δεν θα έχουμε μάθημα ελληνικών.

This is also correct and sounds a bit more explicitly future-oriented, but in this context the simple present is perfectly natural.

Why isn’t there a subject pronoun like εμείς? Would Εμείς την άλλη εβδομάδα δεν έχουμε μάθημα ελληνικών be wrong?

Greek usually drops subject pronouns because the verb ending already shows who the subject is.

έχω = I have
έχεις = you have
έχουμε = we have

So δεν έχουμε already means “we don’t have”; εμείς is usually unnecessary.

You can add εμείς for emphasis or contrast:

Εμείς την άλλη εβδομάδα δεν έχουμε μάθημα ελληνικών, αλλά αυτοί έχουν.
We don’t have Greek class next week, but they do.

So it’s not wrong; it just changes the emphasis.

What does μάθημα ελληνικών literally mean? Why is it ελληνικών and not ελληνικά?

Literally:

μάθημα = lesson / class
ελληνικών = of Greek (genitive plural)

So μάθημα ελληνικών = “lesson of Greek”, i.e. Greek lesson / Greek class.

Ελληνικών is in the genitive plural because Greek commonly uses the genitive after a noun to mean “of X”:

μάθημα μαθηματικών – math lesson (lesson of mathematics)
μάθημα αγγλικών – English lesson
βιβλίο ελληνικών – Greek textbook (book of Greek)

Using ελληνικά (the bare form) right after μάθημα here would sound wrong:
✗ μάθημα ελληνικά is not correct in standard Greek.

So what exactly is the form ελληνικών grammatically?

Ελληνικών is:

Case: Genitive
Number: Plural
Gender: Neuter (but as an adjective used as a noun)

It comes from the adjective ελληνικός, -ή, -ό (Greek), but:

the neuter plural (ελληνικά) is often used as a noun meaning “Greek (language)”
the genitive plural (ελληνικών) then means “of Greek (language)”

So in μάθημα ελληνικών, ελληνικών = “of Greek (language)”.

Could you also say just Την άλλη εβδομάδα δεν έχουμε ελληνικά?

Yes, that’s very common and natural.

In this version ελληνικά is used by itself as a noun meaning “Greek (class / Greek as a subject)”:

Έχουμε ελληνικά. – We have Greek (class).
Σήμερα δεν κάνουμε ελληνικά. – We’re not doing Greek today.

So both are fine:

Την άλλη εβδομάδα δεν έχουμε μάθημα ελληνικών.
Την άλλη εβδομάδα δεν έχουμε ελληνικά.

The second is a bit shorter and more colloquial; the first is slightly more explicit/formal.

Can the word order change, for example: Δεν έχουμε μάθημα ελληνικών την άλλη εβδομάδα? Does that change the meaning?

Yes, that order is also correct:

Την άλλη εβδομάδα δεν έχουμε μάθημα ελληνικών.
Δεν έχουμε μάθημα ελληνικών την άλλη εβδομάδα.

Both mean the same thing.

Greek word order is fairly flexible; changing it usually affects emphasis, not basic meaning.

Starting with Την άλλη εβδομάδα puts emphasis on when.
Starting with Δεν έχουμε emphasizes the fact of not having the class.

In normal speech, both versions sound natural.

Why is there no article before μάθημα? Could it be το μάθημα ελληνικών?

Both are possible, but there’s a nuance:

δεν έχουμε μάθημα ελληνικών
→ we don’t have (any) Greek class; said in a more general / schedule sense
δεν έχουμε το μάθημα ελληνικών
→ we don’t have the Greek class (a particular, specific one you already have in mind)

In schedules, timetables, and habitual statements, Greek often drops the article:

Έχουμε μάθημα στις 8. – We have class at 8.
Δεν έχουμε σχολείο αύριο. – We don’t have school tomorrow.

So μάθημα ελληνικών without το is perfectly standard here.

How are the main words here pronounced and where is the stress?

Syllables are shown with - and the stressed syllable in bold:

Την – /tin/ (one syllable)
άλλη – /Á-li/ (Άλ-λη; stress on the first syllable)
εβδομάδα – /ev-ðo-MÁ-ða/ (ε-βδο-ΜΑ-δα; stress on μά)
δεν – /ðen/
έχουμε – /É-xu-me/ (Ε-χου-με; stress on έ)
μάθημα – /MÁ-thi-ma/ (ΜΑ-θη-μα; stress on μά)
ελληνικών – /e-li-ni-KÓN/ (ε-λλη-νι-ΚΩΝ; stress on the last syllable)

Greek stress is phonemic, so getting the stress right is important for sounding natural and sometimes for distinguishing words.