reformation

IPA: rɛfɝmˈeɪʃʌn

An improvement (or an intended improvement) in the existing form or condition of institutions or practices, etc.; intended to make a striking change for the better in social, political or religious affairs or in the conduct of persons or operation of organizations.
(law) Change or correction, by a court in equity, to a written instrument to conform to the original intention of the parties.
(historical) The religious movement initiated in the 16th century against the Roman Catholic Church.

re-formation

IPA: rifɔrmˈeɪʃʌn

A new formation (a subsequent coming together of the elements of a former grouping)