Brotherhood of Steel
"So tonight, as we break bread together, let us forge together something new. Something strong. Something we can be proud of. Something we can build upon. We'll preserve what's best of what's come before and use it. And one day, we will reclaim what was lost. Let us forge a Brotherhood of Steel"
-Roger Maxon, founder of the Brotherhood of Steel
Formed from the remnants of deserting USA military forces, the Brotherhood of Steel are absolute badasses, and their aesthetic and depictions in the Fallout games are probably the closest direct look at what the early, post-apocalyptic Imperium was really like, with Space Marines being giant rusty metal-men rather than the semi-Roman, colorful, polished gods among men that they now are. If the modern Imperium discovered the Brotherhood of Steel on a random feral planet one day, they would be smoothly adopted into the Imperium, no questions asked. Or, at least the Fallout 4 East-Coast Chapter would. The Fallout 3 version...eh. Some DRASTIC changes would have to be made.
History
Since their founder, Capitan Roger Maxson created them, the Brotherhoods goal was to protect and preserve technology from those who would misuse it, to prevent a nuclear war from ever happening again. They are a group of survivalist soldier-engineers who salvage and protect technology from irresponsible users. Honoring restraint regarding technology and development. I guess this means no stem-cell research?
Witnessing how people around him slowly succumbed to depression, Captain Maxson formulated a new ideology for the survivors. It took him years to create it, replacing the tarnished Stars and Stripes with new symbols, new ranks, and new ideas to replace the ones scorched in nuclear fire. They would provide meaning for people before they became lost in the depths of despair after losing their friends, family, their entire world. Although some under his command, particularly Lieutenant Taggerdy, were skeptical of his plans, Maxson believed that the way forward lay in new traditions and a new mythology, free of the burden of the past. He also believed that it would prevent any surviving politicians from exercising their authority over former American soldiers, especially those with an agenda that involved burning Americans on the funeral pyre of the regime. By June 20, 2082, all members under his command switched over to using Brotherhood ranks and practices.
Like the Imperium, the Brotherhood have armies segregated by their leaders, and deployed across different areas, causing their leaders to make various different policies and practices to form based on their leaders opinions and preferences in terms of how to battle enemies, and how to survive, but all follow the baseline principles created by the founder, Roger Maxon.
The Brotherhood of Steel in Fallout 3 and Fallout Tactics (which IS canon) were much more goody-two-shoes, friendly, underdog super-heroes who fought alongside gross Super-Mutants and undead Ghouls to kill off the epic Enclave, the legitimate remnants of the United States Government (to be fair, they were being lead by an Abominable Intelligence) However after the death of their Boomer leader Elder Lyons, and the effective, but short-lived rule of his daughter who perished in battle, Elder Maxon caused a societal change under his orders for the Brotherhood to become much more f̶a̶s̶c̶i̶s̶t̶ human-centered and focused. Putting the dominant species of Holy Terra first. Operations to wipe out mutated life such as Ghouls and Super Mutants, making things more safe for the people of the Capital Wasteland (once known as the State of Washington) turning it into a militarized city-state.
After recieving reports of a disturbing misuse of technology in the Commonwealth of Massachusetts, Elder Maxon had a great Warship constructed known as the Prydwen, which he became the personal capitan of, and had his best armies shipped off to the Commonwealth, to personally deal with this disturbing abusers of technology, known as the Institute, who would create machines that mimicked real humans perfectly, and were used as workers and spies. Even some loyal Brotherhood Knights were replaced by Synthetic mimicries of life.
There are other endings, but the real ending to Fallout 4 is repairing Liberty Prime, an early Imperial Titan, from his damaged state inflicted upon him from his battles against the Enclave, and using him as a superweapon against the Heretical Institute. Infiltrated through the use of his deadly eye-laser, drilling down underground for the Brotherhood to exterminate the cancer underneath the Commonwealth at its source, halting Synth production when a Nuke was placed inside the Institute, destroying the Institute Scientists and saving the Commonwealth from their experiments. Liberty Prime then just walks in a circle around the Boston Airport, instead of being used to easily cleanse the entire wasteland of Mutants, like he should.
Structure and Ranks
The Eastern division lead by Elder Maxon implemented a heavily modified hierarchy derived from Lyons' Brotherhood of Steel altered ranking system, adapting it to the challenges of the wasteland.
Scribes are the brains to the Brotherhood's brawn. They are responsible for the development and research of all Brotherhood technology, as well as the maintenance of advanced systems, weapons and armor and any other technical requirements.
Squires are children who are too young to train as Initiates but are allowed to serve the various needs of full-fledged members of the Brotherhood. In exchange, they are taught basic concepts such as military structure, combat readiness, and loyalty that will help them when they are old enough to become Initiates. Squires sometimes accompany exemplary Knights on missions, at the behest of Lancer Captain Kells, to experience combat firsthand but only as an observer.
Initiates are Brotherhood-born members and sponsored outsiders who are training to become Knights, Scribes or Lancers.
Aspirant is a rank used to denote someone training under a superior officer such as a Paladin or Knight-Commander in order to be promoted to a full-fledged knight. They are a step above Initiates.
Lancers are the backbone of the Brotherhoods newly formed airforce. Without them, the Brotherhood would be unable to operate their vast fleets of Vertibirds.
Knights are fully-fledged members who have served time in the Brotherhood. They are professional soldiers, and the main backbone of the Brotherhood's ground forces.
Paladins are the Brotherhood's elite, seasoned veterans that are often high ranking field commanders or used in elite strike teams.
Sentinel is a rare rank, only given to the Brotherhood's best and most distinguished soldiers. The last known Sentinel was Sarah Lyons, daughter of Elder Owyn Lyons; she was the highest-ranking field commander under Elder Lyons and commanded the Lyon's Pride, a single squad of the chapter's best soldiers. It is unknown if the Pride still operates as of 2287.
Society
The Brotherhood is a military order with a strictly enforced hierarchy and chain of command. At the foundation of the hierarchy lies the "Chain That Binds" doctrine. It mandates obedience to one's superiors and forbids circumventing ranks when giving orders. Superiors may only give orders to their direct subordinates, but not their subordinate's subordinates. Although intended to ensure the cohesion of command, the doctrine has been generally interpreted as a simple mandate of obedience within the order, with the order flow requirements ignored, abandoned, or altered in practice. However, it does provide a technicality that can be invoked to relieve members of their rank - up to and including elders.
Roger Maxson's goals in inventing a new tradition and mythology for the Brotherhood were two-fold. First, they would ensure that members of the Brotherhood would be stripped of their ties to the pre-War military and government, ensuring that any surviving general or politician would not be able to invoke their oaths and use them to unleash nuclear devastation on the world again (as was the case with Secretary of Agriculture Thomas Eckhart in Appalachia). Second, it would give the survivors an idea to believe in, something they could dedicate themselves to, and finding meaning in their lives after the nuclear war. The inspiration came from the fall of the Western Roman Empire when knights and scribes kept the fire of civilization going after the empire imploded.