Demon (The Relics of Time)

The Demon was an extra-dimensional being hired to set up the planetoid Sepulchre and trap the Fourth Doctor in it. To accomplish this, the Demon staged historical conundrums to get the Doctor to accompany (or follow) him to Sepulchre. If the demon carried a name of his own, he refused to give it.

Description
In most of his appearances the demon took the form of various figures indigenous to the times and places of his traps. He eventually revealed his true form of a large creature with dark purple skin, silvery wings, horns, cloven hooves and a forked tongue. The Demon referred to himself as coming from a place outside the universe we know:

"My home is a tiny backwater in a shadow dimension. A place bearing practically no resemblance to this physical universe."

- Demon

He also refused to offer any real name for himself, stating it would mean nothing to the Doctor.

Powers
Having come from a different dimension, the Demon considered Time to be just another dimension: one among many. The Demon was for all intents immortal. He had a natural ability to change shape and affect the minds of others, though he needed to drain the life force of others to sustain these powers. (AG: The Demon of Paris)

In addition the Demon possessed a high amount of dimensional and psychic technology, which he used to create the Sepulchre atop a planetoid on the edge of the universe. He was able to take pieces of the Doctor's spatial geometer and combine it with cultist chanting to generate a telepath debilitator. (AG: Starfall) He also possessed and used his own primitive version of a TARDIS to move around in time and space. (AG: Sepulchre)

Traps for the Doctor
Having agreed to trap the Doctor, the Demon stole the Doctor's spatial geometer, leaving behind a bag with five objects as clues. The first one, the tile from a Roman mosaic, led the Doctor to Celtic Britain, where the Demon had taken the identity of the Roman Emperor Claudius. Attempts to usher the Doctor inside the back reaches of his tent failed, and the Doctor escaped. (AG: The Relics of Time)

Next, the Demon used an altered version of a poster painted by Henri de Toulouse-Lautrec to lure the Doctor to Paris in the 1890s. In the guise of Lautrec's Concierge he tried to frame Lautrec as a murderer of street girls, in part to cover the Demon's need to feed on those girls. The Concierge almost captured the Doctor in his time craft, but the Doctor managed to force his way out. (AG: The Demon of Paris)

The third object - a storybook with images of the Doctor and Mike Yates in it - drew them to a cave in eastern Europe, where the Demon had set himself up as an Ice Queen with a story teller, Albert Tiermann. Direct threats to Mike did not hold the Doctor, and again the Demon disappeared empty-handed. (AG: A Shard of Ice)

The Demon built a trap in New York City in 1976. He had a meteorite land in Central Park and bestow super-powers to local resident Alice Trefusis. When the Doctor investigated the comic book cover showing the event, the Demon used a telepath debilitator to confuse him. Posing as ageing film star Mimsy Loyne, the Demon almost captured the Doctor, but was foiled when Alice broke up the chanting cultists necessary for the debilitator. In frustration, the Demon kidnapped the Doctor's companion, Fenella Wibbsey outright. (AG: Starfall)

Sepulchre
Following the last item - a golden heart pendant - the Doctor went straight to Sepulchre. The Demon, no longer needing any disguises, sprang the trap on the Doctor. He revealed he was actually working for Mrs Wibbsey, or rather, the Hornets that had regenerated inside of her. The Demon locked the Doctor in a sarcophagus, and started the process to extract all of knowledge of Space and Time from the Doctor's mind, using it to create the Atlas of All Time for the Hornets. A quick turnabout by Mike Yates set Mrs Wibbsey in the sarcophagus instead, quickly destroying the Hornets, the Atlas and Sepulchre. The Doctor, Mike, and Mrs Wibbsey escaped in one direction while the Demon escaped in another direction, free to roam the universe. (AG: Sepulchre)