Can you apply for a Schengen Visa if you plan on staying…

As an international tourist you need a Visa to enter the Schengen Zone but what about European citizens who are not part of the Schengen Agreement?

Citizens of Iceland, Norway, Liechtenstein and Switzerland, which are not part of the Schengen Area, can enter and exit the Schengen states by needing only a national identity card or passport.