The Unification War
Set 500 years in the future, humans have colonized and terraformed a planetary system of unknown location. The system contains "core" planets and "border" planets. As a general rule, the farther out one travels, the less "civilized" society becomes. The core planets eventually allied under a single government, The Alliance, and declared war upon those planets that wished to maintain their independence (The Independent Faction, often referred to as "Browncoats"). This series of events is recalled as the Unification War. The Alliance was victorious, and those surviving independents migrated toward the outer planets.
Battles
Relatively little is known of the actual war itself. Planets and moons in the inner - or core - region of the shows' liveable space had concentrated their power sufficiently that they felt entitled to expand it to the outer societies that had also been planted, but which had had less contact with other worlds since their orbits left them farther away and more isolated. Images of space combat are seen in the feature film Serenity and of the floating aftermath in the 3-issue comic book series Serenity: Those Left Behind.
One of the bloodiest battles of the war was the Battle of Sturges, which, in Those Left Behind, Badger claims was fought over a hoard of money. The lure of that unclaimed cash prize is enough to draw in the Firefly class vessel Serenity and its brigand crew for an ambush. It is known that the Battle of Sturges took place at least partly in space as substantial images of the wreckage are shown in the comic book. Badger suggests that the Battle of Sturges was particularly short ("All those lives... snuffed in a blink"), and describes it as the bloodiest battle of the war, only for Mal to declare it, "a distant second".
In the Unification War the Independents did put aside their own differences to join militaries in the armed forces (including the space ship fleet). The technological and numerical superiority in the war was definitely on the side of the Alliance and the core worlds. Their own undeveloped and isolated pasts were long behind them since they had long ago developed into technologically advanced societies.
Other conflicts mentioned in the series are the Battle of Du-Khang in 2510 (featured in "The Message") and a long winter campaign in New Kashmir. One of the last and most grisly major battles in the war was the Battle of Serenity Valley, in which Malcolm Reynolds and Zoe Alleyne fought (see below).
BATTLE OF SERENITY VALLEY
The Battle of Serenity Valley is considered the final decisive battle in the Unification War. (According to some of the show's canon. In others it is considered the final battle. While in orbit, the Alliance and Independent leaders negotiated a peace, as on the surface soldiers bled, starved and died.) The battle that began in May 2511, while not the final battle of the war, was certainly the end of the line for the Independents, who had sixteen brigades and twenty air-tank squads in position. Taking place on Planet Hera, the battle lasted seven weeks before Independent High Command officially surrendered to Alliance forces. The Alliance won because of superior numbers and a brilliant deep-flank strategy by General Richard Wilkins (a reference to the TV series Buffy the Vampire Slayer). Overall troop casualty rate was 68%. A deleted scene from the film Serenity claims the Independents' command actually surrendered after five weeks of combat, but the soldiers fought on for an additional two before finally giving up. The same is also mentioned in the novelization of the feature film "Serenity" written by Keith DeCandido
Malcolm Reynolds, of the 57th Overlanders, was a sergeant, but by the end of the battle, so many officers had died that he commanded over 5,000 troops. Reynolds and what was left of the army held the Alliance at bay. Their lines were torn and bloodied but holding. Sergeant Reynolds' position was hit hard by a single Skiff that sent all the soldiers closest to him running into their bunker. In a daring move, Reynolds and Zoe Alleyne fought their way to an anti-aircraft turret. The moment Reynolds shot down the attacking skiff he greatly equalized his own position on the front. With his military's own air support on hold (nearby or in orbit), it could be fair to say that Reynolds' heroism won the battle at that moment. Tragically, men of weaker strategic skill were calling the shots for the Independents, and may have given the order to surrender exactly when Reynolds destroyed the skiff. To their dismay, orders came to lay down arms and surrender. What Mal hoped to be the sound of the Independent air support was in fact that of the Alliance cruisers landing. Even though the shooting stopped, the battle was not over. For a week, while the Alliance and Independents sorted out the surrender, Browncoat and Purplebelly (a slang term for Alliance soldiers) alike were left hungry, bloody and dying on field of battle. By the time rescue ships arrived, there were about 150 left of the 5,000 Mal led. He and Corporal Zoe Alleyne were the only two survivors of their platoon.
Malcolm Reynolds' ship, of which Zoe is second in command, is a Firefly-class transport ship, named Serenity after this particular battle; the rubric "no one leaves Serenity, you just learn to live there" being a bittersweet reference less to the ship's status as a home as to the catastrophic bodycount at the battle. The Battle of Serenity Valley is a sensitive issue for both Mal and Zoe, and crew member Jayne Cobb often gets into trouble with the two by bringing up the battle's grim characteristics in an attempt to push Mal.
Participants
THE INDEPENDENT FACTION
"The Independent Faction" was the name of a group that fought the Alliance during the war. The group was nicknamed Browncoats, due to the brown colored trench coats they wore. (Alliance troops were nicknamed "purple bellies" due to the coloring of their own armor.)
One of the reasons they were formed was to attempt and prevent the Alliance from controlling all of the worlds. They did not believe in having all of the planets controlled by a singular government and instead believed in each world's freedom.
The faction was created when the core worlds formed the Alliance and declared war on any planets that resisted their efforts to unify the rest of the planets (thus the name Unification War). After the war ended, surviving faction tended members migrated toward the outer planets, where Alliance control is more tenuous and more of the freedom they fought to defend was preserved.
NOTABLE BROWNCOATS INCLUDE
SERENITY CREW INVOLVEMENT
Throughout the run of the series Firefly, it is revealed what most of the crew members of the ship Serenity did during the Unification War:

