From Longman Business Dictionary
litigatelit·i·gate /ˈlɪtɪgeɪt/ verb [intransitiveI, transitiveT]LAW to take a claim or complaint against a person or organization to a court of lawHe spent several weeks looking for the right lawyers to litigate the case.
litigate againstShe now plans to litigate against the corporation for unfair dismissal.
—litigation noun [uncountableU]The firm now faces litigation from angry consumers.