Name: The Mage's Association
Originated From: Nasuverse 
Leader: No direct leader, rather power is shared among the three branches, which each largely act independently.
Notable Members: 

Clock Tower. (Headquarters and main branch of the Mage’s Association. Clock Tower is currently under the control of a pseudo-aristocratic elite called the Lords.)

The Director. Leader of the Clock Tower for two millennia, a remarkable magus in all capacities.
[url=http://typemoon.wikia.com/wiki/Barthomeloi_Lorelei]Barthomeloi Lorelei[/url]
[url=http://typemoon.wikia.com/wiki/Kayneth_Archibald_El-Melloi]Kayneth El-Melloi Archibald[/url]
[url=http://typemoon.wikia.com/wiki/Waver_Velvet]Waver Velvet, Lord El-Melloi II[/url]
[url=http://typemoon.wikia.com/wiki/Rocco_Belfaban#Rocco_Belfaban]Rocco Belfaban[/url]
[url=http://typemoon.wikia.com/wiki/Bram_Nuada-Re_Sophia-Ri#Bram_Nuada-Re_Sophia-Ri]Bram Nuade-Re[/url]
[url=http://typemoon.wikia.com/wiki/Luviagelita_Edelfelt]Luvia Edelfelt[/url]
[url=http://typemoon.wikia.com/wiki/Rin_Tohsaka]Rin Tohsaka[/url]
[url=http://typemoon.wikia.com/wiki/Gazamy#Gazamy]Gazamy the Spook[/url]
[url=http://typemoon.wikia.com/wiki/Souren_Araya]Souren Araya[/url]
[url=http://typemoon.wikia.com/wiki/Touko_Aozaki]Touko Aozaki[/url]

Sea of Estray. (A conglomerate of minor magi organizations. This base is itself a moving mountain range. Normally it is wandering at sea as its name suggests, but sometimes it comes up on dry land.)
Jewel Killer. Much like The Director, though of a different branch.
[url=http://typemoon.wikia.com/wiki/Cornelius_Alba]Cornelius Alba[/url] (More closely affiliated with the Clock Tower, but rumored as next-in-line for Director of a branch of the Sea)

Atlas Academy. A group of "mathematician" magi who involve themselves little with the other branches, and prefer to sit in place and do calculations about the end of the world. 
[url=http://typemoon.wikia.com/wiki/Satsuki_Kurogiri]Satsuki Kurogiri[/url]
[url=http://typemoon.wikia.com/wiki/Sion_Eltnam_Atlasia]Sion Atlasia[/url]

Anomalies. Those who work with the Association, but are not bound to a specific branch.

[url=http://typemoon.wikia.com/wiki/Gransurg_Blackmore]Gransurg Blackmore[/url]
[url=http://typemoon.wikia.com/wiki/Kischur_Zelretch_Schweinorg]Zelretch Schweinorg[/url]
[url=http://typemoon.wikia.com/wiki/Bazett_Fraga_McRemitz]Bazett Fraga McRemitz[/url]

Notable Weapons/Strengths: 

Enforcers. Magus killers who are based in retrieval of a magus's work when it is deemed necessary to collect by the Association.

Gazamy the Spook, the ultimate anti-magic existence that poses a threat to even the greatest of Casters.

The Seven Great Weapons of Atlas. "Ultimate" weapons created by the mathematicians, the seal on Atlas that must absolutely never be lifted.

Kaleidosticks and other assorted Mystic Codes of Zelretch's, as well as Class Cards meant to emulate the abilities of Heroic Spirits.

Variability of magi in terms of their power and ability, though this can be seen as detrimental due to a lack of communicative ability.