Captain Aldis is the captain in the Imperial Legion and in charge of the Solitude Guards. When you first arrive in Solitude he is personally overseeing the execution of Roggvir. He can normally be found pacing the courtyard of Castle Dour. If you side with the Stormcloaks he will leave the game entirely after the Battle for Solitude.
Upon meeting him, he asks you to bring him a copy of The Mirror, a book dealing with shield training.