The Master

The Master, like the Doctor, is a Time Lord. To use an Earth literary analogy, he is somewhat of a Moriaty to the Doctor's  Holmes. He has been described as "one of the most evil and corrupt beings (the) Time Lord race has ever produced ("The Five Doctors")."

Early Life on Gallifrey
The Master was one of the Doctor's classmates at the Time Lord Academy. During this time they appear to have been close friends. It was probably during this time that he also first met the Rani. Following graduation, the Master pursued a career as a Magistrate for the High Council ("The Infinity Doctors").

Descent into Darkness
"The Dark Path"

The Master vs. the Doctor and UNIT
Sometime after his previous encounter with the Doctor, the Master appeared at a circus ground on Earth in the 1970s, his TARDIS materializing in the form of a circus trailer or horse box. He promptly hypnotized the circus troupe to obey his orders, as part of his plan to assist the Nestenes in their latest bid to conquer Earth ("Terror of the Autons"). Over the next few years, he and his hypnotized or otherwise suborned followers engage in several attempts to conquer the Earth, often with the aid of alien invaders. However, his attempts were invariably foiled by the Doctor.

Living Death
When the Fourth Doctor encountered the Master on Gallifrey, he had exhausted his supply of regenerations and was attempting to rejuvenate himself; this theme of acquiring a new cycle of regenerations appears throughout the Master's future battles with the Doctor. The Doctor later learned in his eighth incarnation that the Master exhausted his regenerative cycle recovering from injuries suffered on Tersurus in an explosion triggered by Susan Foreman when he attempted to kidnap her ("Legacy of the Daleks").

A New Body at Last
The Master, while on Traken managed to take over the body of Tremas, Nyssa's father. In this new form, he continued his efforts to conquer the universe; but he was also focused on acquiring a new cycle of regenerations, rather than finding ways to take over new bodies.

Eventually, he was tried and executed by the Daleks; but he was somehow able to take over the body of an ambulance driver on Earth, in spite of having been reduced to a small quantity of fluid. (Doctor Who: The TV Movie)

The End?
At the end of his battle with the recently regenerated Eighth Doctor, the Master fell into the Eye of Harmony, and was presumably destroyed. The Doctor claimed that he had been eaten by the TARDIS. It should be noted, however, that the Master has seemed on many previous occassions to be completely destroyed, only to return, becoming even more evil and dangerous each time.