Hope this adds a better light on things Narceron.
The 501st Legion, later known as "Vader's Fist" and the Five Hundred and First, was an elite unit of clone troopers and later stormtroopers. Commissioned by Supreme Chancellor Palpatine during the Clone Wars, the 501st fought in many battles, such as the Battle of Mygeeto and the Battle of Coruscant, becoming one of the most well-known and most feared legions. In 19 BBY, the legion became Darth Vader's personal stormtrooper unit as he led them during Operation: Knightfall, in which the clones helped take down the Jedi, whom they believed to be traitors to the Republic.
Following the rise of the Galactic Empire, the 501st transitioned into a stormtrooper unit, like all other clone units. Given new armor and weapons, the 501st faithfully served the Empire, operating under the direct command of Darth Vader. The legion fought in a number of battles during the Galactic Civil War in an effort to defeat the Rebel Alliance, although the Alliance ultimately triumphed. However, the 501st would continue to serve the Empire, fighting under the command of leaders like Grand Admiral Mitth'raw'nuruodo.
After the Battle of Kamino, the 501st became the last remnant of the Grand Army of the Republic fully composed of clones of Jango Fett, as opposed to the ever-growing and more diverse Stormtrooper Corps, where the Fett clones became a minority with the inclusion of a pool of clones from different templates and birth-born recruits. Eventually, under the Chiss Grand Admiral Thrawn, more diverse recruits would be added to the 501st, including non-Humans.
A member of the 501st constructed a journal of his thoughts during some of the most well-known battles in which he fought.
