An engineer constructed or repaired buildings and mechanical devices. There were a number of specialised types of engineers.
Omega was the stellar engineer who gave the Time Lords the source of power for time travel. (TV: The Three Doctors)
Ben Travers was an engineer working at the Fang Rock lighthouse in 1902. He was attacked and killed by a Rutan scout. (TV: Horror of Fang Rock)
John Dyson was the supervising engineer at the Snowcap South Pole Base in 1986. He, Barclay, Ben Jackson and Haines used radiation to fight the Cybermen. (TV: The Tenth Planet)
Van Lutyens was an engineer at a Euro Sea Gas Control Rig. He fell under the weed creature's mental control, but was eventually freed thanks to the Second Doctor. (TV: Fury from the Deep)
Bill Duggan was an engineer on Space Station W3. (TV: The Wheel in Space)
Dervish had been an engineer for the Earth government before joining Maurice Caven's band of space pirates. (TV: The Space Pirates)
Eckersley and Vega Nexos were mining engineers stationed on the planet Peladon. (TV: The Monster of Peladon)