The General Ministry was the bureaucracy of the Galactic Republic. It was organized into several large permanent Ministries, smaller task-oriented service Agencies, and several semi-independent Institutes. The various Senate councils had oversight and financing authority over the corresponding Ministries.
The General Ministry oversaw a wide variety of concerns, including the ministries of government, finance, commerce, intelligence, and science and education. The latter segment placed a number independent institutes and universities, termed the General Ministry Institutes, under its oversight. The General Ministry was directed by the First Administrator.
Presumably after the Declaration of a New Order, It was reorganized and placed under the authority of Emperor Palpatine's top advisors through the Grand Vizier and the Imperial Ruling Council. During the New Republic, it was most likely succeeded by the Alliance Cabinet, then later the New Republic General Ministry.