Τον Σεπτέμβριο έχω πάλι μάθημα ελληνικών στο πανεπιστήμιο.

Because Greek often uses the accusative case with time expressions like months when it means in September.

• ο Σεπτέμβριος = September as a dictionary form, nominative
• τον Σεπτέμβριο = in September

So Τον Σεπτέμβριο is a very common way to say in September.

You may also see τον Σεπτέμβρη, which is a more everyday version of the month name.

Τον is the masculine singular accusative definite article, meaning the.

It agrees with Σεπτέμβριο, which is masculine. In this sentence, the article is part of the time expression:

• τον Σεπτέμβριο = in September

So even though English does not say the September here, Greek normally uses the article in this structure.

Yes, έχω literally means I have. But in Greek, έχω μάθημα is a very common expression meaning:

• I have class
• I have a lesson
• I have a course

So έχω πάλι μάθημα ελληνικών is not about possessing a lesson; it means that classes start again, or that the speaker has Greek class again.

Greek often uses μάθημα in the singular where English might use class or classes, depending on context.

• έχω μάθημα = I have class / I have a lesson
• έχω μαθήματα = I have classes / lessons

In this sentence, the singular sounds natural and can refer to the subject or class as a regular activity. It does not necessarily mean there is only one single session ever.

Because ελληνικών here means of Greek / Greek language, not Greek as a general adjective.

• μάθημα ελληνικών = Greek lesson / Greek class
• literally: lesson of Greek

This is a very common Greek pattern: a noun followed by another noun in the genitive.

Examples:

• μάθημα αγγλικών = English lesson
• καθηγητής μαθηματικών = math teacher
• βιβλίο ιστορίας = history book

If you said ελληνικό μάθημα, that would more likely mean a Greek lesson in the sense of a lesson that is Greek in character, not necessarily a lesson in the Greek language.

Ελληνικών is in the genitive plural.

The basic form is:

• τα ελληνικά = Greek, the Greek language

When it follows μάθημα, it changes to the genitive:

• μάθημα ελληνικών = lesson of Greek

This is a standard structure in Greek for school subjects and areas of study.

Πάλι means again.

So the sentence suggests something like:

• I have Greek class again in September
• In September I have Greek again at university

It can imply that the class stopped for a while, for example over the summer, and then starts again.

Greek word order is fairly flexible, and πάλι can move depending on emphasis.

In this sentence:

• Τον Σεπτέμβριο έχω πάλι μάθημα ελληνικών στο πανεπιστήμιο.

the focus is natural and neutral.

Other possible word orders include:

• Τον Σεπτέμβριο πάλι έχω μάθημα ελληνικών στο πανεπιστήμιο.
• Πάλι έχω μάθημα ελληνικών τον Σεπτέμβριο.

These may sound slightly different in emphasis, but the core meaning stays similar. The original version is a very natural choice.

Στο is a contraction of:

• σε = in / at / to
• το = the

So:

• σε το πανεπιστήμιο becomes στο πανεπιστήμιο

It means:

• at the university
• in the university, depending on context

In English, at the university sounds more natural here.

It is in the accusative singular.

The noun is:

• το πανεπιστήμιο = the university

After σε, Greek uses the accusative:

• στο πανεπιστήμιο = at the university

This is normal Greek grammar:

• στο σπίτι = at home
• στη δουλειά = at work
• στο σχολείο = at school

Yes. Greek word order is more flexible than English word order, because case endings show the grammatical relationships more clearly.

The sentence starts with the time expression:

• Τον Σεπτέμβριο = In September

This puts the time frame first, which is very natural. Then:

• έχω πάλι μάθημα ελληνικών = I have Greek class again
• στο πανεπιστήμιο = at the university

So the order is:

1. time
2. verb
3. rest of the information

That is a very normal Greek way to build the sentence.

Yes, but it is usually omitted because the verb already shows the subject.

• έχω = I have

So Greek does not need εγώ unless you want emphasis or contrast.

Compare:

• Τον Σεπτέμβριο έχω πάλι μάθημα ελληνικών στο πανεπιστήμιο. = neutral
• Τον Σεπτέμβριο εγώ έχω πάλι μάθημα ελληνικών στο πανεπιστήμιο. = I have Greek class again in September, maybe unlike someone else

Yes. In context, it can cover several similar meanings:

• a Greek lesson
• a Greek class
• a Greek language course session

Greek often leaves that slightly broad, and the exact English translation depends on context. In this sentence, Greek class or Greek lesson both work well.