Brigadier Alistair Gordon Lethbridge-Stewart first encountered the Doctor as a Colonel, during the Yeti invasion of London. When the much-loved Colonel Pemberton was killed, Lethbridge-Stewart took over the operation from him, and soon encountered the Doctor wandering the Underground tunnels. Following the Yeti invasion, Lethbridge-Stewart was promoted to Brigadier, he grew a moustache, and he was put in charge of UNIT. When the third Doctor was exiled to Earth, the Brigadier invited him to join UNIT as its scientific adviser, and so they worked closely together for years.
As a military man, the Brigadier is accustomed to order, structure and obedience, and is therefore frequently bewildered and annoyed with the Doctor's subversive and haphazard methods. Although the Brigadier values the Doctor's help, and the Doctor appreciates the Brigadier's friendship and resources, both men frequently butt heads. The Brigadier has a quick temper, and is easily infuriated by anything he perceives as incompetence or disobedience. There are frequently times when the Brigadier just can't figure out what on earth the Doctor is talking about, and his frustration with himself usually redirects itself into anger at the Doctor!
The Brigadier is a very stubborn person, both in following orders - as any good military man should be - and in holding his own in arguments with the Doctor. He is also quite opinionated, and once he has made up his mind about something, it is difficult to sway him. Sometimes Jo, with her puppy-dog eyes and gentle voice, has more luck with him, but more argumentative Doctor and Liz are usually out of luck. However, the Brigadier almost always yields to authority, and if his superiors advise him to do something, he obeys.
The Brigadier's motto seems to be "when in doubt, blow it up!" The Doctor, of course, is vehemently opposed to it, but the Brigadier would rather destroy a potentially dangerous enemy than treat it with kid gloves and be killed later. He does, however, bemoan the fact that most of the alien creatures he encounters are impervious to bullets!
But for all their conflicts, the Brigadier is very loyal to the Doctor, and is willing to do anything he can to help, as long as it does not contradict his standing orders. Generally the Brigadier puts all of his resources at the Doctor's disposal, because he trusts the Doctor deeply and knows that the Doctor's methods get results. Amusingly, the Brigadier is by nature a skeptical person, and although his mind is hugely broadened by his time in UNIT, he is still initially unwilling to believe some of the more outlandish things he experiences (such as being transported to alien worlds).
Eventually the Brigadier retires from UNIT, replaced by Colonel Crichton, and begins teaching mathematics at Brendon public school, where one of his students - the shifty Turlough - ends up joining the Doctor on his travels. The Brigadier retires from teaching and begins a peaceful domestic life with his wife Doris, although he remains on inactive duty in case his help is ever needed again.
