Professor Carter Nichols

Pre-Crisis

Professor Carter Nichols was a friend of the Golden Age Batman and Robin. Using a technique he developed, called time travel hypnosis, Prof. Nichols was able to send people back in time mentally, but not physically. He often assisted Batman and Robin on cases. For example, investigating why ancient Chinese fireworks go off in the shape of Batman, or going into the future to meet the Joker's sane descendant,. Rekoj, who had become the chief of Police in Gotham.  Later, Nichols invented a time-ray that is capable of actually sending people foreward or backwards in time. 
 
Nichols was also the mentor to Wendy and Marvin in the Superfriends comics.
 

Post-Crisis

During the time in which Thomas and Martha Wayne were murdered, Carter Nichols was a doctor at the Willowood millitary Asylum, Gotham's asylum after Arkham was closed and before it was reopened. He used his experimental Time Hypnosis to help veterans with PTSD overcome their troubles.  The chief of Willowood, Dr. Simon Hurt, offered Nichols untold riches or anything else he wanted in exchange for his assistance in a Religion of Crime / Black Glove rite. That night, Hurt, Nichols, Marsha Lamarr,  and John Mayhew tried to kill the time tossed Bruce Wayne and summon the demon Barbatos using Nichols' Time Box device.  The rite was going videotaped with Mayhew posing as Thomas Wayne and Lamarr as Martha, in an attempt to ruin the deceased couple's reputation.
 
However, Nichols ultimately decided that his "soul is not for sale". Bruce Wayne, dressed in a repica of Thomas' Bat-Man costume, broke free from his restraints and grabbed the Time Box, tossing him through time and apparently bonding him with Barbatos. Hurt said that though Nichols had won the Black Glove's wager of good vs. evil, he would now wallow in obscurity for the rest of his life, where he could have had untold riches and fame.
 
Early in Batman's career, a group of villains attacked Nichols and forced him to send Batman backwards in time to retrieve items for them. For instance, for Catwoman, the combination to an ancient Egyptian safe, or for the false Mad Hatter, the brim size of Alexander the Great. This version of Nichols uses a special helmet called a Maybe Machine to assist in the time hypnosis- it allows the wearer to see visions of what could have happened. After Batman breaks free form the restraints that the villains have him held in, the police arrive before anyone appears to have contacted them.
 
Later, during Dick Greyson's time as Batman, Prof. Nichols is found dead in his lab behind a locked door.The corpse he left behind is several decades to old to be Prof. Nichols. The truth behind this is revealed in Damian Wayne's  time as Batman. When a villain called 2 Face 2  holds the city for ransom using a climate control system, Damien tracks him down and finds he is holding an infant Terry McGinnis and an elderly Carter Nichols hostage- Baby New Year and Old Father Time.
 
Following Damian defeating 2 Face 2, the Carter Nichols from Bruce's time arrives. He kills the future Nichols because of how the Joker had humiliated him during during the aforementioned heist, then takes the body back to Dick's time before calling the police in Bruce's time.
 

Animation

Batman: Brave and the Bold

 
Prof. Nichols appears in an episode of Brave and the Bold, "The Last Bat on Earth!". He is assaulted by Gorilla Grodd, who forces him to use his Time Ray to send him into Kamandi's future to team up with the gorilla armies there. Nichols sends Batman into the future to fight Grodd.