Assuming you're asking about Western Christian monks:
- The majority of monks would be addressed as Brother.
- The leader of a monastery is an Abbot, and is addressed as Father. The Abbot himself addresses monks as 'my son'. A Prior is one step down from the Abbot. Some monasteries are big enough to have Subpriors who are yet another step down. (As an aside, a monastery which is big enough to have an Abbot is called an Abbey; one which isn't is called a Priory.)
- A monk in training is a Novice. A candidate to be accepted as a Novice is a Postulant. They are both referred to by their first names.
- The title 'Fra' is sometimes used for monks but more properly refers to friars, wandering monks.
- In some orders of monks, the title 'Dom' is used to honor monks who have distinguished themselves,
- Technically, nuns are also monks; in their case the equivalents would be Sister instead of Brother, Abbess instead of Abbot, Mother instead of Father, Prioress instead of Prior, and 'Dame' instead of 'Dom' (Women were almost never friars).
- Other titles exist, such as Definitor, Provost, Circator, and Dean, which are used differently by different Monastic Orders.
- The technical term for a monk is a 'Cenobite'. Absolutely nobody says this.
Although the vast majority of monks of all faiths and denominations are called Brother (or Sister) in English, other monastic systems, such as Eastern Orthodox Christian and Buddhist monks, have their own sets of titles.
