Collecting Radiation
The foremost function of any telescope is to collect and focus some form of radiation. This radiation may be light, radio waves, X-rays or other forms of energy. This collected energy is focused onto a viewing apparatus. The viewing apparatus may be the human eye, in the case of a standard optical telescope, or a computer-aided visualization mechanism. The latter is often used when viewing energy other than visible light.
Non-optical Observation
Telescopes allow for energy unrecognizable by the human eye to be observed. Radio telescopes, for example, allow for the observation of radio waves within the cosmos. This type of telescope is responsible for the discovery of many of the most high-energy celestial objects in the cosmos, such as quasars, pulsars and supernovas. Telescopes designed to collect non-optical energy allow you to map planets that are not observable directly due to cloud cover, such as Venus.
Optical Observation
Standard optical telescopes are primarily used to view astronomically close objects, such as the solar planets. They are also used in navigation to ascertain the distance and direction of faraway objects. Orbiting telescopes, such as the Hubble Space Telescope, allow astronomers to observe celestial objects with little interference from the atmosphere of Earth. This allows for much higher resolution images to be obtained of celestial bodies and the spaces between them.
Search for Extraterrestrial Life
Telescopes allow for monitoring of energy not only as images but also as structured emissions. These energy emissions are analyzed by scientists in the search of life beyond Earth. The largest radio telescope on Earth, located in Arecibo, Puerto Rico, is used by researchers at Berkeley University to study radio transmissions from space in an attempt to locate intelligent patterns indicative of purposeful radio transmissions from another species.
Spectroscopy
Telescopes allow scientists to identify normally unobservable objects at great distances and ascertain their characteristics, such as velocity, chemical composition and approximate size. All matter absorbs, emits and transmits electromagnetic radiation when exposed to it. The reflection of this radiation to Earth from astronomical distances is collected with a telescope and passed through a prism to spread the radiation into what is known as a spectrum. From this spectrum, scientists can determine the chemical composition of the material being observed, because all material absorbs and reflects only specific types of the radiation it is contacted with. Further, the red or blue shifting of this spectrum can be used with Doppler calculations to determine the movement and rotation of the object.