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How to throw a gift wrapping party 
Stick to simple invites. 
A gift wrapping party, in essence, is about getting together with friends to have fun doing something that can be tedious and time consuming. Since this is a for-fun activity, there's no point in stressing over fancy invites.
A simple email to your friends and family should be more than enough to get the ball rolling in your party planning. If you plan on this gift wrapping party to be a more elegant affair, there's nothing wrong with putting together formal invitations for your guests.