Transcendental engineering is 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.
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 SIDRAT's, though only through the intervention of a renegade Time Lord, Magnus. (DW: The War Games)