Telescope

Telescopes were devices for looking at things from a distance. "spyglass"' was a name sometimes applied to handheld telescopes. (PROSE: The Empire of Glass)

The Doctor's telescope
On Dulkis, the Second Doctor was about to view some ruins with a folding telescope when Jamie McCrimmon took it from him. He then returned it after using it to examine the ruins. (TV: The Dominators)

On another planet, the Second Doctor used a folding telescope to observe a train pull into a station. (COMIC: The Exterminator)

On Solos, the Third Doctor used a folding telescope to survey a Solonian village. (TV: The Mutants)

The Fourth Doctor gave Leela a telescope in Australia. (PROSE: The Bushranger's Story)

On Shontaa, the Fourth Doctor used a telescope to observe the duel between the Zygons Anktra and Kestral. (COMIC: Rest and Re-Creation)

On Pluto, the Fourth Doctor used a folding telescope to admire Megropolis One and noted it to be "an engineering achievement". (TV: The Sun Makers)

The Fourth Doctor and Romana I used a folding telescope to observe Zanak's control centre, the Bridge. The telescope was later confiscated from Romana by a guard, who described it as "a forbidden object". (TV: The Pirate Planet)

The Fourth Doctor used a telescope to locate the Jagaroth ship in Earth's primordial past. (TV: City of Death)

The Fourth Doctor used a telescope to observe the spaceship Hydrax from afar. (TV: State of Decay)

The newly-regenerated Seventh Doctor found a telescope in his former incarnation's coat pockets. (PROSE: The Useful Pile)

On Kirith, the Seventh Doctor used a telescope to survey Kirith town and its environs. He then gave the telescope to Miríl. (PROSE: Timewyrm: Apocalypse)

The Doctor's TARDIS had a telescope observatory. (TV: Journey to the Centre of the TARDIS)

Other telescopes
Early astronomers used telescopes to observe the stars and planets. In Alexandria a group of astronomers saw skyships. (COMIC: Voyager)

In the late 15th century, Giuliano developed a primitive telescope, which the Fourth Doctor deemed merely adequate. (TV: The Masque of Mandragora)

In the early 17th century, Galileo Galilei invented the telescope. (PROSE: The Empire of Glass)

In the mid-1950s, he Tenth Doctor and Martha Jones visited the Griffith Observatory. The Doctor charged up the observatory's telescope to show Martha the last residual image of Gallifrey from before the Last Great Time War. (COMIC: Quiet on the Set)

In 1959, Jerome Weismuller used a folding telescope to watch for a satellite. (TV: Delta and the Bannermen)

The people of Sarn used telescopes. Peri Brown made use of a fixed telescope in order to search for the Fifth Doctor. (TV: Planet of Fire)

The Sixth Doctor used a fixed telescope aboard Voyager's "Death-ship" to follow Astrolabus's escape. (COMIC: Voyager)

Rezaul Kapoor owned a telescope which he and his sister Anji once used to observe Mars. (PROSE: Fear Itself)

Eugene Jones owned a telescope, which he used to watch for aliens. (TV: Random Shoes)

Wilfred Mott owned a telescope, which he frequently used. (TV: Partners in Crime) In a parallel world, he offered to sell it for extra money, but Donna Noble was firmly against it. (TV: Turn Left)

On Braktalis, Demimon witnessed the arrival of Skrant's ship while observing the stars through his telescope. (COMIC: The Outsider)

References to telescopes
Richard Dunbar told the Fourth Doctor that if he had seen anything like the Krynoid pod before, he must have a very powerful telescope. (TV: The Seeds of Doom)