There are many types of telescopes, who developed the first one ever, I do not think we will ever know. There are many people who say it was them. Different designs were invented by different people.
One famous design is the Newtonian, by Isaac Newton, the first mirror is a concave mirror which means it is shaped like this (. The second mirror is a small flat one only a few cm in diameter. The light travels down a tube, hits the ( shaped mirror, then reflects back up the tube and hits the small flat mirror (at 45 degs) and is bounced out the side, where you can look at the image. You will need an eyepiece in order view the image. But that is all that is in the basic telescope, 2 mirrors and an eyepiece.
Galileo is the man who is most commonly credited with building the first telescope, but it is believed that they were quite easy to buy in Holland around that time. What is for sure is that Galileo was the first person to use it to view the heavens. He discovered the four largest moons that orbit Jupiter so these are now known as the Galilean moons. This was a huge deal be=cause at the time almost everyone believed that the Earth was the centre of the Universe, and that everything went around the Earth. Galileo showed that there were objects that did not go around the Earth, but rather around Jupiter. As Stephen said, Newton greatly improved the design by switching from lenses to mirrors!