The Brown Ajah of the Aes Sedai is devoted to knowledge and the collection of ancient wisdom. They generally forsake the mundane world, instead dedicating themselves to history and study, and are responsible for the administration of the White Tower Library. The Brown Ajah is run by a ruling council, the head of which is called First Chair.
The Blue Ajah of the Aes Sedai normally involve themselves with righteous causes and justice. They have the most extensive eyes-and-ears network, and enjoy the prestige of having the highest number of Amyrlin Seats raised from their Ajah. The Blue has been at odds with the Red Ajah for a millennium, and for a time were separate from the White Tower altogether. The head of the Blue Ajah is called the First Selector.
The Asha'man from the Black Tower - Wheel of Time
The Red Ajah of the Aes Sedai is dedicated to locating men with the ability to channel and bringing them to the White Tower for gentling. Red sisters generally do not have friends outside of their Ajah, and upon donning the shawl are often forced to end any friendship with women not also of the Red. They bond no Warders, and have been at odds with the Blue Ajah for a millennium. The leader of the Red Ajah is known as the Highest.