Few characters in all of fiction have had their life story told as thoroughly as Anakin Skywalker, but the official Darth Vader timeline still has plenty of gaps in it. Unless one has delved into the extended lore of Star Wars - the novels, the comics, the video games, and more - they likely have little idea what happened to Darth Vader after Revenge of the Sith but before A New Hope, and that alone represents nearly two decades of the Sith Lord’s physical existence.
As any good supplementary material should, Vader’s extended universe content only serves to deepen and expand upon his persona. Some of Vader’s best moments have come off-screen and between movies, and while it’s not required reading in order to appreciate the character, it is necessary if one wants to fully understand him - lest he find your lack of detailed knowledge disturbing.
19 BBY: Vader Defeated Jedi Master Kirak Infil'a So He Could Take His Lightsaber's Kyber Crystal
19 BBY: Vader Eliminated The Jedi Librarian Jocasta Nu
19 BBY: Vader Took Over The Sith Inquisitorius And Joined Them On Missions To Track Down The Remaining Jedi
18 BBY: Vader Survived A Bounty Placed On His Head And Took Out His Rage On His Imperial Rivals