You may already know the word عزم يعزم 3azam yi3zem ‘invite’ (not ‘be determined’ as in fuSHa), but unless you’re German or Turkish this simply gloss is likely to expose you to some misunderstandings and possibly some embarrassments without a little bit of cultural background. If you tell someone:
بعزمك على فنجان قهوة
bi3zmak 3ala finjaan 2ahwe
‘I’ll invite you for a cup of coffee’
You’re more or less saying ‘I’ll buy you a cup of coffee’.
If someone says to you:
اكيد عزمتو بعد ما فادك هيك
2akiid 3azamto ba3d ma faadak heek
[You must have invited him after he did that for you]
What they mean is ‘you must have bought him dinner/bought him a drink after he did that for you’.
If after going out for coffee (or whatever) with someone they say:
انا عازمك
2ana 3aazmak
I invited you
They’re offering to pay. It’s polite to do this and then argue about it for a bit before one of you concedes (this can be a fairly awkward social thing to get used to, but it gets easier). Conceding immediately makes you look rude. This is a broader field of social awkwardness too, since even if you don’t explicitly say one of these expressions, you might (emphasis on might) be expected to pay if you invite someone somewhere.
The noun is عزيمة عزايم 3aziime 3azaayem ‘invitation’. Sometimes you might be invited (out of politeness) to have dinner somewhere, or just not be able to attend. Something you can say is:
عندي عزيمة
3indi 3aziime
‘I have an invitation’
معزوم عند غيرك
ma3zuum 3ind gheerak
‘I’m invited to someone else’s [house]’
Ideally being apologetic.