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With the information we have, you probably qualify for the Research visa.
You'll find all the info and how to apply, in the official Italian visa site
Assuming a random citizenship, you need (this might change from nationalities to nationalities) :
So I need some kind of letter or invitation in the application?
Yes, you would have needed that for any type of visas (if you don't show that you will have your visa denied). Either a proof of enrollment or signed letter from someone there that certifies you have enrolled in the course
You'll find the localized info here on VFS UK site