Αν καθυστερείς, στείλε μου μήνυμα για να μην ανησυχώ.

Αν means if.

It introduces a condition: If you are late / if you’re delayed...

In everyday Greek, Αν is the normal word for if. You may also see Εάν, which is a more formal or slightly more emphatic version, but Αν is much more common in speech.

καθυστερείς is the 2nd person singular present active form of καθυστερώ, meaning to be late, to delay, or to run late depending on context.

So:

• καθυστερώ = I am late / I delay
• καθυστερείς = you are late / you are running late

Here it addresses one person informally, so it means you’re running late or you’re delayed.

In Greek, after Αν, the present tense is very often used for a real or likely future condition, especially in everyday language.

So Greek says literally something like:

If you are running late, send me a message...

Even though English may also use the present after if, learners sometimes expect a future form. Greek normally does not use a future marker here.

So Αν καθυστερείς is the natural way to say If you’re running late.

στείλε is the singular imperative of στέλνω (to send).

It means send!

This is the command form used when speaking to one person informally.

Examples:

• στείλε μου = send me
• στείλε μου μήνυμα = send me a message

This imperative is based on the verb’s perfective stem, which is why it looks different from στέλνω.

μου means to me / my, depending on context. Here it means to me.

Greek often uses these short weak pronoun forms before or after verbs, and with imperatives they usually come after the verb:

• στείλε μου = send me
• πες μου = tell me
• δώσε μου = give me

So:

• στείλε μου μήνυμα = send me a message

This is completely natural Greek word order.

Yes. μήνυμα means message.

In modern everyday Greek, it can refer to:

• a text message
• a message in an app
• a general message

So στείλε μου μήνυμα is very natural and common. In many contexts, English speakers might translate it more specifically as text me or send me a message.

You could also hear:

• στείλε μου ένα μήνυμα = send me a message

The article/number word ένα is optional here.

για να means so that or in order to.

It introduces a purpose clause.

So:

• στείλε μου μήνυμα = send me a message
• για να μην ανησυχώ = so that I won’t worry / so I don’t worry

Very literally, the structure is:

Send me a message in order that I not worry.

This is a very common Greek pattern:

• για να δω = so that I can see
• για να πάω = so that I can go
• για να μην αργήσουμε = so that we don’t arrive late

Greek uses μη(ν) for negation in certain non-indicative structures, especially with:

• imperatives
• subjunctive clauses
• purpose clauses with να

Since ανησυχώ here is in a να-clause after για να, the correct negative is μην.

So:

• δεν ανησυχώ = I am not worrying / I don’t worry
• να μην ανησυχώ = that I not worry / so that I don’t worry

A useful shortcut:

• δεν usually negates ordinary statements
• μη(ν) usually negates commands, wishes, and να-clauses

Yes. After να, Greek uses the subjunctive.

In modern Greek, the subjunctive is usually marked by να, not by a completely different verb ending. In many verbs, the form looks identical to the present indicative.

So:

• ανησυχώ = I worry / I am worrying
• να ανησυχώ = that I worry / so that I worry
• να μην ανησυχώ = so that I don’t worry

The verb form itself looks the same, but να tells you it is functioning as a subjunctive.

Because the person speaking is talking about their own reaction.

The logic is:

If you’re running late, send me a message so that I don’t worry.

So:

• καθυστερείς = you are late
• στείλε = send
• μου = to me
• ανησυχώ = I worry

Greek is tracking two different people in the same sentence:

• you in the condition and command
• I in the purpose clause

Yes, the comma is normal and correct.

Greek, like English, usually separates an introductory if-clause from the main clause with a comma:

• Αν καθυστερείς, στείλε μου μήνυμα.

It helps show the structure clearly:

1. condition
2. main action

Yes. A few very natural alternatives are:

• Αν αργήσεις, στείλε μου μήνυμα για να μην ανησυχώ.
  This uses αργήσεις from αργώ, another common way to say be late.

• Αν καθυστερήσεις, στείλε μου ένα μήνυμα.
  Here καθυστερήσεις is a more punctual/perfective form: if you end up being delayed / if you’re going to be late.

• Αν αργείς, στείλε μου μήνυμα.
  Slightly shorter, and the purpose so I don’t worry is just understood.

But the original sentence is already completely natural and idiomatic.