The Amrothian Society of the Wand

The Amrothian Society of the Wand is a tightly organized, hierarchical, order of wizards based in Dol Amroth. They offer many benefits to wizards including a wizard school, item creation, libraries, material components, scrying devices, a teleportation circle to some other location, and planar binding areas where younger wizards may practice their summoning skills.

The school, called The Illumination, is probably the most well known school of wizards in Aeriador, save for the Tower of Sorcere and the Sorcerer's Enclave in Rhune. Graduates of The Illumination are called Illuminati and become full members of the Amrothian Society of the Wand. 

The complex of the Society is vast, with many halls, chambers, massive cathedral like rooms, an Inn and Tavern, magic stores selling nearly all material components and many lesser and mundane magical items. There is a museum of magical artifacts and art collections from ages past and the Hall of Sorcerers has paintings of many prominent wizards from long ago.

The rank structure within the Society of the Wand is broken down into the various schools of magic and the level of spells a wizard is able to cast.

For example, a specialist wizard in the school of illusion who can cast 4th level arcane spells might be called an Illusionist of the 4th Order, or a 4th Order Illusionist.

Generally speaking, necromancy and evil spells are forbidden to be practiced on the complex. 

The various schools and their titles:

Abjuration = Abjurer

Conjuration = Conjurer

Divination = Diviner

Enchantment = Enchanter

Evocation = Evoker

Illusion = Illusionist

Necromancy = Necromancer

Transmutation = Transmuter

Universal = Wizard

Casters of the 1st Order through the 4th Order have no additional rank

Casters of the 5th Order through the 7th Order are called Mages and are considered senior ranking casters within the Society

Casters of the 8th and 9th Orders are called Archmages and are the highest ranking and most powerful casters in the Society

A full designated title might look something like this (name, class, order, rank if any)

Bilbo, Enchanter of the 5th Order, Mage of Enchantment, in a social setting with other wizards, especially students, he would be addressed as "Mage Bilbo" or "Mage Enchanter Bilbo"

A student at The Illumination wizard school might be called:

Pippin, Wizard of the 2nd Order, and he would be addressed by lower ranking students as "Wizard Pippin"

The current head of Illusion is the First Wand of Illusion, the Archmage Nicodemus Courtemanche. He is a very typical looking wizard with white hair and beard, carries a staff and a wand, and dresses in an eccentric robes and hat. He is an 8th Order Archmage of Illusion.