Μην βάλεις το ποτήρι πάνω σε αυτό το βιβλίο.

Μην is the word used for a negative command in Greek, meaning don't.

So:

• Βάλε το ποτήρι... = Put the glass...
• Μην βάλεις το ποτήρι... = Don't put the glass...

In Modern Greek, negative commands are usually formed with:

• μη(ν)
  • subjunctive-type verb form

That is exactly what is happening here.

This is one of the most important things learners notice.

The basic verb is βάζω = I put.
But after μη(ν) in a negative command, Greek normally uses the aorist subjunctive form, not the ordinary present form.

So:

• βάζεις = you put / you are putting
• βάλεις = form used here after μη(ν), from the aorist stem

This verb is a little irregular:

• present stem: βαζ-
• aorist stem: βαλ-

That is why βάζω becomes βάλεις here.

Not exactly in form, but yes in meaning.

Greek often avoids using a true imperative form in the negative. Instead, it uses:

• μη(ν)
  • subjunctive

So although the sentence functions as Don't put..., grammatically it is built differently from a positive imperative.

Compare:

• Βάλε το ποτήρι... = positive command
• Μην βάλεις το ποτήρι... = negative command

This is very normal Greek.

Yes, very often you can.

The negative particle appears as μη or μην. In everyday Greek, both are heard in many cases.
Μην βάλεις is completely correct, and μη βάλεις is also very common.

For a learner, the safest thing is:

• recognize both
• understand that both mean don't

πάνω σε means on, on top of, or onto, depending on context.

In this sentence:

• πάνω σε αυτό το βιβλίο = on this book

Literally, πάνω has the idea of up/on top, and σε is the preposition on/to/in depending on context. Together they commonly mean on.

So this is a very natural way to say that something is physically resting on a surface.

Because πάνω σε is more specific.

• σε by itself can mean in, to, at, or sometimes on, depending on context.
• πάνω σε clearly shows on top of a surface

So:

• σε αυτό το βιβλίο could feel less precise
• πάνω σε αυτό το βιβλίο clearly means on this book

This is normal Greek structure.

Greek usually says:

• αυτό το βιβλίο = this book
• εκείνο το βιβλίο = that book

So the demonstrative (αυτό) is followed by the definite article (το) and then the noun.

English does not do this, but Greek does.
It is not extra or redundant — it is simply the standard pattern.

Both are in the accusative.

Why?

• το ποτήρι is the direct object of βάλεις
• αυτό το βιβλίο comes after σε, and σε takes the accusative in Modern Greek

So:

• το ποτήρι = accusative singular neuter
• αυτό το βιβλίο = accusative singular neuter

For neuter nouns like ποτήρι and βιβλίο, the nominative and accusative forms are often the same, so you do not see a visible change.

Because it has to agree with βιβλίο.

βιβλίο is:

• singular
• neuter
• accusative

So the demonstrative must match it:

• masculine: αυτόν / αυτός depending on function
• feminine: αυτή / αυτήν depending on function
• neuter: αυτό

Here, αυτό το βιβλίο is the correct neuter singular form.

Yes, Greek word order is more flexible than English, although this sentence is the most neutral and natural order.

Standard order here:

• Μην βάλεις το ποτήρι πάνω σε αυτό το βιβλίο.

You might also hear variations for emphasis, such as:

• Το ποτήρι μην βάλεις πάνω σε αυτό το βιβλίο.
• Μην βάλεις πάνω σε αυτό το βιβλίο το ποτήρι.

These can sound more marked or emphatic.
For learners, the original version is the best one to use first.

Yes: the stress is on the first syllable:

• βάλεις

This matters because stress is important in Greek pronunciation and meaning.

A rough pronunciation guide for the whole sentence is:

• MEE(n) VA-lis to po-TI-ri PA-no se af-TO to vi-VLI-o

That is only approximate, but it helps show where the stress falls.

It breaks down like this:

• Μην = don't
• βάλεις = put
• το ποτήρι = the glass
• πάνω σε = on
• αυτό το βιβλίο = this book

So the grammar pattern is:

• negative command
  • verb
    • object
      • place phrase

This is a very useful pattern to learn, because you can build many similar sentences from it, for example:

• Μην βάλεις το κινητό πάνω στο τραπέζι. = Don't put the phone on the table.
• Μην βάλεις τα κλειδιά πάνω στην καρέκλα. = Don't put the keys on the chair.