To “serve notice” - *very* formal giving (serving) of notice of, e.g., writs

To “give notice” is used in most/all cases when a court is not somehow connected, e.g., giving notice to a landlord/counterparty/friend of some intention; to serve notice in such cases would, to most people, not be correct English, although some would say it’s ok (http://idioms.thefreedictionary.com/serve+notice)