Traveling with permesso di soggiorno for 6 months in the EU

What is your permesso di soggiorno for?  study/work/dimora?  The visa allows you to tsay in  Europe, the PdS is for a specific country within Europe, but gives you rights throughout the Schengen zone.  You need the visa to get your PdS and then (within limits) you are like a temporary EU citizen.

Thank you but I have the pds for studying. and I have been reading  that I just can travel 3 months in every 6 months, but I think it is not correct and I didn't find anything for it that is written officially

As it stands you won't be able to travel anywhere soon in the EU at the moment due to COVID.

I may be wrong but I think you need an identity card - carta di identità - which would show you are a resident of Italy. A permesso di soggiorno is NOT an ID.  You also don't say what your nationality is. As I understand it if you are extra-EU you cannot stay in Europe for more than three months but if you are a resident you can. You should take your permesso and go to the anagrafe in whatever city you live in and apply for a carta d'identità. Then you can travel throughout Schengen within that time period.

@Modicasa Hey, My study visa (1 year) is only for Italy. Once I get my PDS, can I travel across the Schengen area?

@Modicasa Hey, My study visa (1 year) is only for Italy. Once I get my PDS, can I travel across the Schengen area?
-@lifethroughsana

Together with a valid passport yes, but you may not work in any Schengen country.

@Modicasa Hello,I am in italy with a long term study visa, italian visa not schengan. Is it possible for me to travel EU schengen countries with just a PDS card?

@Cynic I am in italy with a long term study visa, italian visa not schengan. So it is possible for me to travel EU schengen countries with just a PDS card and my passport?

@Cynic I am in italy with a long term study visa, italian visa not schengan. So it is possible for me to travel EU schengen countries with just a PDS card and my passport?
-@lifethroughsana

If you have a valid PDS and passport from your own country, then you can use that to travel within the 27-member Schengen Zone, not all EU countries are in Schengen, this link will take you to the Schengen website where you can see which countries are signatories.  You can only use this scheme to visit the countries, you may not work, or call on any social support (i.e. healthcare) while visiting.