Like the Doctor, the Monk is a Time Lord - in fact, one of the first that the Doctor encounters after fleeing Gallifrey. But that is not all. The Monk, quite simply, is a time meddler. Rather than sit idly by, he finds it much more fun to interfere with history and see what happens. He keeps a diary of his adventures, which are really quite notable. The Monk met da Vinci and discussed the principles of powered flight with him; he deposited £200 in a London bank in 1963 and then went forward 200 years to collect a fortune in compound interest; and, he contributed an antigravitational lift to the ancient Britons' attempts to build Stonehenge. The Monk uses a progress chart to keep track of his agenda. He keeps a collection of artefacts from every period and every place that he visits. These are stored in a Mark IV TARDIS, which the Monk was able to obtain as he left Gallifrey 50 years after the Doctor did. His TARDIS has such impressive features as an automatic drift control that allows him to suspend himself in space with absolute safety - the Doctor, naturally, is very jealous. And although it has a functioning chameleon circuit, on the inside it looks just like the Doctor's.
Despite his unwise fixation with changing the course of history, the Monk is not malicious - he actually only wants to improve things. This is not to say that he doesn't have his bad points - he is amazingly immature, quite cunning and terribly irresponsible. He will betray his allies if need be, and is often quite rude, though he may act friendly.
During his escapade in 1066, the Monk wore a traditional monk's habit with a large ring on the index finger of his right hand...and a twentieth-century wristwatch. True to his nature, he cares little for the damage that could be done to the timeline by his casual ignorance. The eleventh century was littered with things like phonographs, modern cooking devices and advanced medication during his stay of residence there.
When the Monk first arrived in 1066 - feeling that Harold would be an excellent King of England - he first moved into a local monastery and set up a phonograph to play records of monks chanting, but did not speak with the villagers. He kept his TARDIS disguised as a sarcophagus. He eventually requested that the villagers keep a fire constantly lit on the cliff, planning to use this as a method to lure the Vikings in to the shore. Once they arrived, he intended to destroy their ships with a laser cannon. With the Vikings out of the way, Harold would be able to focus on defeating William the Conqueror at the Battle of Hastings. The Doctor, however, let the villagers in on his little scheme. While they stormed the monastery and chased the Monk off, the Doctor removed the dimensional control circuit from his TARDIS - leaving it the same size inside and out, and the Monk marooned in 1066.
The Monk was eventually able to bypass the dimensional controller, and escaped from 1066 determined to exact revenge upon the Doctor. He finally caught up with the Doctor on the planet Tigus, where his TARDIS disguised itself as a rock. The Monk attempted to disable the Doctor's lock and strand him on Tigus, but the Doctor quickly reversed his sabotage, so the Monk tracked him to ancient Egypt (and brought along his mirrored sunglasses).
In Egypt, his TARDIS disguised itself as a stone building block for the pyramids. While the Monk was out tracking down the Doctor (and running into the Daleks), the Doctor slipped into his TARDIS and altered its exterior into an Ionic column, then a stagecoach, a small tree, an igloo, a one-man rocketship, a camel, and finally, a police box just like the Doctor's. Meanwhile, the Daleks persuade the Monk to con his way into the Doctor's good graces and steal the taranium core of their Time Destructor from him. The Monk attempts this, but the Doctor quickly sees through his charade and seals him up in an Egyptian sarcophagus, bound in mummy wrappings.
The Daleks do not look kindly on the Monk's failure, but he claims to have brought them Steven and Sara as hostages, so they spare his life. The Doctor manages to bargain for the lives of all three in exchange for the taranium core; upon gaining his freedom, the Monk flees Egypt, but finds himself on a planet of ice, with his TARDIS disguised as an iceberg. During his sabotage of the Monk's TARDIS exterior, the Doctor also removed his directional unit, leaving the Monk as unable to control his TARDIS as the Doctor is.