In the civil law. A notification to a party that some step in a legal proceeding is asked or will be taken. Particularly, a notice given by the party taking an appeal, to the other party, that the court above will hear the appeal.
In Scotch law. A formal written notice, drawn by a notary, to be served on a party against whom a stranger has acquired a right or claim; e.g., the assignee of a debt must serve such a notice on the debtor, otherwise a payment to the original creditor will be good.