Transdimensional engineering

Transcendental engineering was the technology of creating dimensionally transcendental objects, which the Fourth Doctor proclaimed a "key Time Lord discovery". (DW: The Robots of Death) It enabled TARDISes to exist.

Other than the Time Lords, the Daleks (DW: The Chase, The Evil of the Daleks) and Mawdryn's people, who sought to emulate the Time Lords, had developed this technology and employed it in their transmat capsules. (DW: Mawdryn Undead) Oddly, the Cult of Skaro refered to this as "Time Lord Science" which suggest that they too, emulated them. (DW: Doomsday)
 * It was established in Doomsday that the Genesis Ark is actually a Time Lord prison ship that was 'rescued' by the Cult of Skaro prior to the end of the Time War.

A young Trion officer seemed unfazed by the dimensionally transcendental interior of the Doctor's TARDIS, which suggests his species had some familiarity with this kind of science. (DW: Planet of Fire)

The War Lords possessed dimensionally transcendental space-time vessels known as SIDRATs, though only those provided by a renegade Time Lord, the War Chief. (DW: The War Games)