What was the book of rules to be used for governing monasteries called?

Most monasteries in the Western branch of the Church are based on The Rule of St. Benedict. There are several major branches of Benedictines, Cistercians, and Cistercians of the Strict Observance (Trappists), plus Camoldese, etc. who all follow The Rule of St. Benedict. In addition to The Rule, each congregation has specific Constitutions and Directories. You may see the Constitutions and Directory for the American-Cassinese Congregation of Benedictines at the link below. Eastern rite monks usually follow The Rule of the Master which is much longer than The Rule of St. Benedict.