i have a cyprus id card and im studying in milan can i travel to...

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...amsterdam with my cypriot id.? im going on hollydays in may ..im a student at milan im going to amsterdam on may and i only have my cypriot id card can i travel only with the cypriot id???
from cyprus to milan i showed only my id card and it was ok i mean i think with an id card from n eu country u can fly to all europe right ?so how can it be poseble to fly from cyprus to milan with my id and from milan to amsterdam i would need a passport? thank u...