Absolutely. This is a classic high school physics project. Just remember that your results are going to reflect the budget and time spent on the project.
You could grind your own glass lenses painstakingly for days, and hand fit nice brass parts, or you could drop a few acrylic lenses in a pvc pipe assembly. The latter will be a telescope, but it’s no hubble.
The simplest telescope is just two lenses. You could buy two different magnifying glasses at the hardware store, but the magnification of the scope will depend on the focal length of your lenses. It may be worth experimenting with a few.
There’s nothing magical about telescope technology and it’s common for kids to make them in elementary school with paper towel rolls and magnifying glasses. Generally speaking, something that people could construct on their own in the 17th century can still be constructed in the 21st.
If you want to literally make one from scratch you would need to carve and polish the lenses yourself, but otherwise you can gather the parts and find instructions with no trouble.
Yes, lots of people over on r/telescopes or r/atming have done this and can give detailed answers if you actually plan on doing it. You can order premade lenses or mirrors to the specs needed and assemble it (or grind the optics yourself if you really want to DIY it).
Also keep in mind there are [several different types of telescopes](https://sas-sky.org/wp-content/uploads/2011/09/SAS-Types-of-Telescopes.pdf) with pros and cons for each type.
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