Gallifreyan technology

Gallifreyan technology included time travel devices (such as the TARDIS), as well as other significant inventions.

Abandoned technologies
Gallifreyans experimented with tachyonics before abandoning that field in favour of warp matrix engineering. (TV:  The Leisure Hive) Time Lords also experimented with hyperspace, but finally abandoned it as a theoretical absurdity two thousand years before the Doctor's time (TV: The Stones of Blood)

TARDISes

 * See TARDIS

APC Net

 * See APC Net and the Matrix

Dimensional transcendentalism
The Time Lords had the ability to make objects that were bigger on the inside than on the outside. This technology was used for TARDISes and for some Time Lord prisons.

Behind the scenes
This information about hyperspace conflicts with several known examples of other species successfully using hyperspace technology (e.g. humans in TV: Frontier in Space).