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 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 an alternate timeline, he offered to sell it for extra money, but Donna Noble was firmly against it. (TV: Turn Left)

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)