A Brief History
All mages outside of the Chantry sanctioned Circles are considered Apostates, and Dalish mages are also considered apostates, since by definition they are not controlled by any Circles. Solas is most definitely an apostate, though he has the distinction of not even being a Dalish mage. He does not agree with the Dalish, and has lived by himself and learned magic on his own. With his interests in studying spirits in the Fade, he has knowledge in areas most other mages avoid or fear.
Both the Circle and the Dalish have long and complicated histories in Thedas, the world in which Dragon Age exists. Long ago, the ancient elves lived in a glorious empire, but when that empire collapsed, many elves were enslaved by the Tevinter Imperium. One human slave, the prophet Andraste, guided by the great Maker and with help from an elven slave named Shartan, led a rebellion that eventually freed many slaves, and upon her betrayal and death, the Andrastian Chantry was formed.
For their help, the elves were given the Dales, a fraction of the land that was once a part of the ancient elven empire, Elvhenan. They made the perilous trek, and the ones who survived the journey called the city they founded Halamshiral, "the end of the journey," where many other elves would eventually go, attempting to reclaim their culture. Fearing human incursion, the elves isolated themselves until a skirmish between elves and humans triggered a full scale war—in what was later known as the Exalted March of the Dales—led by Orlais and with the support of the Chantry. Outnumbered by the Orlesian Empire forces, the elven forces were eventually crushed and their territories swallowed by Orlais, leaving those surrendering to accept the religion of the Chantry and the Maker and renouncing their own ancient elven gods. Those who reside in human settlements across Thedas were forced to live in squalor in districts called Alienages, and are collectively referred to as city elves.
Not all elves accepted this, and those who rejected living amongst humans in the alienages chose to instead live out on their own, reclaiming what was lost and calling themselves the Dalish, and forming a collection of autonomous clans. Dalish clans follow an hierarchy of being led by a Keeper, who is a mage, and followed by a successor, known as the First of the clan.
Dalish mages are self-trained and study magic based on remnants of the old ways, though their views on the Fade and demons are very similar to that of the Chantry and their Circles.
On the other side, the Circle of Magi was formed by the Chantry as a way to regulate and protect mages from themselves and others. As mages receive their gift from their connection to the Fade, it also opens them up to demonic possession from demons across the Veil, and the Chantry has decided certain magic to be dangerous. To control mages, who have such powers, the Chantry ordained the Templar Order to watch over and hunt down any renegade mages. The Templars were established through the Nevarran Accord, which unified the original Inquisition with the Chantry as the latter's military arm. The Inquisition then split into the Templars and the Seekers of Truth, which became the Templar Order's regulatory force.
Mages in the Circles are taken from their families at a young age (be it human nobles, peasants, or elves who live in the alienages) and sent to live in the cloistered towers to train and serve, separate from and sometimes feared by the rest of society. All mages must pass the Harrowing when they come of age and have gone through the necessary magical training. Apprentices who do not pass the test are either killed by Templars or turned Tranquil. Those who aren't confident in their abilities may elect to go through the Rite of Tranquility rather than taking the Harrowing and risking death. While the details of the Harrowing are kept secret from apprentices, tranquility is considered a "safe" alternative to the dangers of demonic possession, as being made tranquil cuts off all connections a mage may have to the Fade. Cutting off a mage's connection to the Fade will prevent them from demonic possession, but cutting mages off from their source of magic has the side effect of causing them to lose all sense of emotion and personality, rendering them prone to obeying commands and following a logical path in life. Some see tranquility as a safe alternative to the dangers of the Fade, while others view it worse than death. This counterpoint would eventually lead to the Mage-Templar War, when a faction of Circle mages rejected the oppression in the Circles as well as the constant threat of the Rite, electing instead to be independent.