Batman: The Killing Joke
Possible the most influential book of any series in relation to one of its established characters being changed forever. This was a rebirth for the Joker, as we were given a window into his madness. In a trial of bloody violence we follow Batman as he attempts to defeat the Joker. Moore's Joker is unlike any before, as he is attempting to prove that "One bad day" is all it takes to make a sane person go insane. This includes crippling and then sexually assaulting Barbara Gordon (Batgirl). This is at the nexus of Heath Ledger's performance as the Joker in The Dark Knight. It is not for the faint of heart nor is it for kids. But it is for those who want to gain an insight into want can make you go insane and into the mind of the murderous man who laughs.
Honourable Mentions: Batman: Year One by Frank Miller and David Mazzucchelli, Batman: The Man Who Laughs by Ed Brubaker and Doug Mahnke and Batman: The Cult by Jim Starlin and Bernie Wrightson. There was much that I had to omit for this introductory guide to Batman. And as I said before the scope of the DC Universe is vast; there is a Batman story out there of everyone. So if you are new to the world outside of the films, check out the items on this list and see how deep you wish to go into the world of Bruce Wayne.