The 2006 edition of the Oxford Dictionary of Law:
"The part of the law that deals with such aspects of relationships betwen individuals that are of no direct concern to the state. It includes the law of property and trust, family law, the law of contract, mercantile law and the law of tort."
Similarly, Jowitt's Dictionary of English Law suggests that the term civil law is synonymous with private law:
"Private or civil law deals with those relations between individuals with which the state is not directly concerned: as in the relations between husband and wife, parent and child, and the various kinds of property, contracts, torts, trusts, legacies, the right recognized by the rules of admiralty, etc."
Private law is the counterpart to public law.
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