This is the The Penguin disambiguation page. Find what you want and go away.
The Penguin is Oswald Cobblepot, an infamous crime lord who operates out of Gotham City. As the owner of the Iceberg Lounge, the Penguin runs much of the illegal gambling and arms dealing that goes through Gotham. The Penguin is constantly battling Batman and the GCPD in a desperate and hopeless attempt to prove that he's not just a funny little dwarf with a top hat.
The Penguin's primary choice of weapon is an umbrella, which probably doesn't help is public relations issue. When he's not using the umbrella, he uses adorable little penguins with bombs strapped to their chests, so there's that too.