Solas is an elven apostate mage who has never lived in a mage circle. His expertise centers around Elvhen history and the fade and he appears to speak fluent Elvhen. Unlike most other Elves in Thedas, he is classed neither as a city elf nor Dalish elf, choosing to instead roam the world in search of places of historical interest where he can practice his unique lucid dreaming magic where he can explore places as they once were whilst dreaming in the fade.
Solas is one of the characters introduced to the inquisitor during the tutorial segment of the game, and will remain with the inquisition up until the endgame, regardless of his approval rating.
Solas will form a positive relationship with any inquisitor who is curious, and respects spirits (who solas has several friendships with, and believes to be as human as any being on thedas). He dislikes closed mindedness, and will approve decisions made to support mages and elves.
Solas also approves the player character displaying knowledge, and also activating the Elvhen artifacts he will remark on when nearby if he is in your party.
[Plot spoilers for Dragon Age: Inquisition]
Solas joins the inquisition shortly after the Breach opens, and arrives in time to prevent the Mark on the player character from killing them whilst unconscious. When meeting the player character for the first time after this event, he is with Varric Tethras and shows the Player Character how to close small rifts before accompanying them to the Temple of Sacred Ashes to attempt to close the main Breach.
When the Breach is stabilized after the Player Character sides with the Mages or Templars, Solas announces that he will stay with the Inquisition, and reveals some knowledge he has about the Orb used by the Elder One, that it was Elven and used by ancient Elves to channel their powers, before leading the Inquisition to Skyhold, a long lost castle.
Solas remains in Skyhold whenever he is not in the Inquisitor's Party, and he paints a mural in the Rotunda depicting wolves as the main story progresses.
In Skyhold, Solas will trigger a conversation with the Inquisitor in the fade which looks like Haven, where character development along with insights into Solas's motivation can be found, along with the first opportunity for a Female Elf Inquisitor to trigger the possibility of a romance.
Solas's personal quest will also trigger shortly after reaching Skyhold, where he will ask for the inquisitor to save a spirit friend of his who has been summoned against their will by some apostates. What occurs after this will greatly affect his Approval rating, and in the case of a Female Elf, possibly remove the chance of a romance occurring with Solas.
If Solas is taken to the Winter Palace during Wicked Eyes and Wicked Hearts, he will remark how much he enjoys the "heady blend of power, intrigue, danger and sex" later on. He is announced to the court as "Lady/Lord Inquisitor's Elven Servant, Solas".
If Solas is taken to the Temple of Mythal, he and Abelas will tell the Inquisitor of the true fall of Arlathan, translate some Elven along with Morrigan, and offer unique dialogue options with Abelas.
Solas will hold the broken orb after Corypheus is defeated and express his sadness that the orb could not be saved. If he was the Inquisitor's romance choice, he will offer some further parting words before disappearing beyond where Leliana's agents could track him. Either way, Solas is not part of the inquisition in the endgame, and his Tarot card reflects this.
In the Epilogue scene, Solas meets with Flemeth and apologises, revealing he was the one who gave Corypheus the orb used to create the Breach. He says the people still need him, and Flemeth apologises as well before collapsing in his arms, where it is unclear what happens, but it appears Solas absorbs the essence of Flemeth.
During this exchange Flemeth refers to Solas as "The Dread Wolf", another name for one of the Elvhen Gods, Fen Harel. This final plot twist is expected to be covered at some point either in the next Dragon Age game, or in a future DLC.