The Master is another renegade Time Lord, pretty much the polar opposite of the Doctor. The Doctor fixes things. The Master fucks them up. A while back he used up his share of incarnations -- 13? -- and spent a while as a rotting hulk plotting in his (newer and working) TARDIS. Finally he stole a new body and was off again.

The two actually worked together on at least one occasion -- someone had messed with the equations that ran the Universe, and it was coming apart, and they figured out that compromising was preferable to dying.