Lazlo Valentin or Professor Pyg is the leader of the Circus of Strange.
Professor Pyg is a deranged schizophrenic who has developed an obsession with making people "perfect", which he accomplishes by transforming them into Dollotrons, a process that bonds false "doll" faces to their own, presumably permanently. Professor Pyg uses cordless drills, hammers and ice picks along with the "doll" faces in the process of converting his victims into Dollotrons. It appears the operation he performs involves brain surgery or a form of lobotomization and possible gender realignment. Behind his mask he is a middle-aged Caucasian male. He wears a simple pig mask and is often depicted wearing a makeshift surgical outfit.
Morrison describes the character as "one of the weirdest, most insane characters that's ever been in Batman. We hear a lot about Batman facing crazy villains but we tried to make this guy seem genuinely disturbed and disconnected." The character name is a shortened form of Pygmalion.
In Batman and Robin issue 2 he proclaims the "Year of the Pig" at the end of the issue as his minions capture Robin. It is revealed in issue 3 of Batman and Robin that Pyg was attempting to release an addictive identity destroying drug in the form of a virus into Gotham through infected Dollotrons. He initially sold the drug/virus to gangs who were using it to control prostitutes. Finally realizing its potential he intended to hold the city for ransom. His plan is foiled when Batman (having extracted his whereabouts from Phosphorus Rex) confronts him at his hideout. Batman arrives at Pyg's disused fun fair hideout to discover Robin, who had previously run off after an argument, there too. Robin, having just escaped from Pyg's efforts to convert him into another Dollotron, works with Batman in subduing Pyg. Pyg is arrested and taken to Arkham Asylum where he currently resides.
In the non-canonical future of Batman #666 he is found by the police without his mask and crucified.
Powers and Abilities
Pyg does not have any superhuman powers or abilities. He is however, an extremely skilled surgeon.
In Other Media
There is a Professor Pyg reference when the Balloonman is about to kill his first victim, he dons a hoodie and pig mask, also, Gerald Crane's accomplice wears a costume similar to Pyg.
But in season 4, Pyg (played by Michael Cerveris) finally makes an appearance, murdering crooked cops while wearing a pig mask ("Hog Day Afternoon"), and tricking the cops and Penguin's loosely allied gangsters into an embarrassing trap while manipulating Jim Gordon into playing the hero ("A Day in the Narrows").
The Gotham version of Pyg does not appear (so far) to have surgical skills. Instead, he so far seems to be a very effective trap-maker, have a source of information in the mob and/or the GCPD, and be a master of disguise.