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Faster-than-light travel was one method of travelling interstellar distances faster than the speed of light. One way to do so was by harnessing a quantum tunnel with an FTL factor of 36.7 recurring. (TV: School Reunion)
The Eleventh Doctor once sent proof of faster-than-light travel with two diagrams and a joke to experts of the world to prove he was a genius. (TV: The Eleventh Hour)
Most advanced civilisations seemed to have developed faster-than-light travel at some time during their history. Humans developed their first lightspeed ship in the late 21st century, (TV: The Waters of Mars) faster-than-light ships in the mid-22nd century (AUDIO: Leviathan) and had developed hyperspace technology by the 30th century. (PROSE: Original Sin)
The Monarch wanted to discover the secret to faster-than-light travel to travel back to the creation of the universe and meet God, whom he believed would be himself. (TV: Four to Doomsday)
Examples
Common means of faster-than-light travel involved passing a spacecraft through hyperspace, which was located outside of space-time as humans knew it. (TV: The Stones of Blood) Other technologies included warp drive. (TV: The Girl in the Fireplace, Earthshock)
The Nestene Consciousness used warp shunt technology to travel between planets. The Ninth Doctor told the Nestene to use the technology and "shunt off!" (TV: Rose)
The people of the Arcateen system used superluminal technology, specifically communications and travel technology, to transport themselves to other planets and communicate over great distances. (TV: Greeks Bearing Gifts, Invasion of the Bane)
Raxacoricofallapatorians had slipstream engine technology. (TV: Aliens of London / World War Three)
The ships of the Uvodni (TV: Warriors of Kudlak) and the Adipose (TV: Partners in Crime) could travel at faster than light speeds.
The Daleks achieved faster-than-light travel early on in their history in space. Their prototype spacecraft Proto 4 was destroyed when it attempted faster-than-light travel, and Proto 9 succeeded but was destroyed when it came out of hyperspace. However, Proto 13 was successful and became the first fully successful attempt by the Daleks in their efforts to achieve space travel. It was successful in take off, space flight, and entering/exiting hyperspace. It had a flying saucer design, and became the standard Dalek ship. (COMIC: The Amaryll Challenge)