Transcendental engineering was the technology of creating dimensionally transcendental objects which The Doctor proclaimed this 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 refer to this as "Time Lord Science" which suggest that they too, emulated them. (DW: Doomsday) (It is 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 through the intervention of a renegade Time Lord, the War Chief. (DW: The War Games)