Telescopes
Invented in Holland at the beginning of the 17th century, telescopes are the tools used by astronomers and astrophysicists for their observations. With the development of modern science, telescopes are nowadays used for observing in all ranges of the electromagnetic spectrum, inside and outside Earth's atmosphere. Telescopes work by collecting light with a large surface aerie called objective that makes the incoming light to converge. The final image will be viewed by using an eyepiece.

Aperture and Focal Ratio
Telescopes are used in order to collect light from celestial objects and to converge it to a point, named the focal point. They are described by two parameters, aperture and Focal Ratio. The diameter of the light collecting surface is called the aperture of the telescope – the bigger the aperture, the brighter the image. The ratio of the focal length f to the aperture D of a telescope is defined as the focal ratio. This describes the light gathering power of a telescope. Fast telescopes have smaller focal ratios, as they obtain brighter images in a smaller exposure time. As the focal ratio gets bigger, the telescope needs more exposure time in order to obtain a bright image, which is why it is slower. The focal ratio is usually denoted as f/n, where n is the ratio of the focal length to the aperture.

Aberrations
In order to obtain an image, telescopes use lenses or mirrors. Unfortunately, if we use both of them we obtain image distortions known as aberrations. Some aberrations are common for both lenses and mirrors, like astigmatism and curvature of field.
Astigmatism appears when different parts of the lens or mirror make the rays of the incoming light to converge in slightly different locations on the focal plane. When corrected for astigmatism, curvature of field may appear on the surface of the lens/ mirror, which makes the light to converge on a curve rather than on a plane.
Still, there are also lens specific aberrations and mirror specific aberrations.
Chromatic aberration is a feature of telescopes that use lenses to converge the light. Mainly, the focal length of a lens is wavelength dependent, which means that the focal point of blue light differs from that of the red light. This results in a blurred image. The effect of chromatic aberration can be diminished by adding correcting lenses into the system. Spherical aberration may also be a problem for lenses, resulting from their shape. Spheroid surfaces will not make the incoming light to converge to a single point, which is why other optical surfaces like paraboloids are preferred. Even by using them we aren't still out of trouble, as coma aberration appears in this case. It results from the dependence of the focal length on the angle between the direction of the incoming ray and the optical axis of the system. Thus, images of points that lie off the optical axis are elongated, rather than being simple points, as it would be normal.

Magnification
Magnification, the increase in angular size of an object as viewed in a telescope, is described as the ratio of the focal length of the objective to the focal length of the eyepiece. So the greater the focal length of the objective, the greater the magnification. If you want to have a large image then you need a long focal length objective and a short focal length eyepiece.
As an example, if you have a 500 mm objective and a 25 mm eyepiece the resulting magnification will be 500 / 25, which is 20, or 20X.

Field of View
The field of view is the angle covered on the sky by the telescope.The apparent field of view of a telescope is determined only by the eyepiece. It is a specific characteristic of it, usually around 52 degrees. In order to find the true field of view of a telescope, you need to divide the apparent field of view by the magnification. The true field of view is the actual angle covered on the sky by the telescope.
has a tool to find and display (on the virtual sky) a true field of view called the FOV Indicator. Launch it by heading under the Settings FOV Symbols Edit FOV Symbols... menu item. Clicking New... will open a dialog with four different tabs: Eyepiece, Camera, Binocular and Radiotelescope. To compute the field of view, select the tab that applies and enter the specifications of the equipment. Finally, clicking Compute FOV will calculate and display the field of view immediately below. can now also display this as a shape of that size on the virtual sky. To do so, enter a name for this particular field of view (such as 20mm eyepiece or DSLR with refractor) and select a shape and color to be displayed. For Eyepiece, use Circle or Semitransparent circle as the shape since an eyepiece's field is round. For Camera, use Square (which is actually a rectangle) assuming the sensor or film is rectangular or square. When using multiple eyepieces and/or telescopes, it is good to distinguish them with different colors. Click OK to close the dialog. To show the shape on the screen, go back under the Settings FOV Symbols submenu, then select the new menu item with the name of whatever it was given. To disable it again, click the menu item again.

Types of Telescopes
As telescopes are used in observations over the entire electromagnetic spectrum, they are classified in Optical Telescopes, Ultraviolet, Gamma Ray, X-Ray, Infrared and Radio Telescopes. Each one of them has its own, well defined role in obtaining a detailed analysis of a celestial object.

Optical Telescopes
Used for observations in the visible field of view, Optical Telescopes are mainly Refractors and Reflectors, the difference between the two of them being the way of collecting light from a star.
Refracting Telescopes use two lenses in order to create an image, a primary or objective lens, which collects the incoming light, forming an image in the focal plane and the eyepiece, which is acting as a magnifying glass used for observing the final image. The two lenses are situated at opposite ends of a moving tube and the distance between the two of them can be adjusted in order to obtain the final image.
The largest refracting telescope in the world is at the Yerkes Observatory in Williams Bay, Wisconsin. Built in 1897, it has a 1.02-m (40-in) objective and a focal length of 19.36 m.
Reflecting Telescopes, on the other side, use mirrors instead of lenses in order to obtain the final image. By replacing the objective lens with a mirror, we obtain a focal point that lies on the path of the incoming light. An observer situated at this point could see an image, but he would block part of the incoming light. The focal point of the principal mirror is called prime focus, and this is also the name of the first category of reflecting telescopes. Thus, prime focus telescopes use a mirror in order to collect light from a celestial object and by reflection the image of the object may be observed from the prime focus of the telescope. Other types of reflecting telescopes are Newtonian, Cassegrain and Coude.
The Newtonian one uses an additional flat mirror placed in the vicinity of the prime focus, in the path of the reflected light. This results in moving the focal point to a different location, on one of the sides of the telescope, more accessible for observing. Of course, a mirror placed in the path of the reflected light will also block part of the incoming one, but if the ratio of the surface aeries of the primary mirror to the second one is big enough, the amount of the blocked incoming light is negligible.
The Cassegrain telescope is similar to the Newtonian one but this time the secondary mirror reflects light to the bottom of the telescope. There is a hole at the center of the primary mirror that lets the reflected light to go on its way until it converges to the focal point. The secondary mirror needs to be convex, as it is increasing the focal length of the optical system. The primary mirror of a Cassegrain Telescope is a paraboloid. By replacing it with a hyperboloid we obtain a Ritchey-Chretien telescope. The advantage of using a Ritchey-Chretien telescope is that it removes the coma of the classical reflectors.
The Coude type consists of more than one mirror that reflects the light to a special room, the Coude room, which is located below the telescope. The advantages of using a Coude telescope are varied, from obtaining a long focal length useful in different fields of astronomy and astrophysics, like spectroscopy to avoiding the usage of a massive instrument. But there are also disadvantages in using a Coude telescope, because the more mirrors are placed in the system, the less amount of light arrives at the detector. This happens because by using Aluminum mirrors, only 80 % of the incident light gets reflected.
Catadioptrics are types of telescopes that use systems of both lenses and mirrors for making the light to converge. The most popular catadioptric is the Schmidt-Cassegrain telescope. It has the advantage of providing a large angle field of view. In order to minimize coma, it uses a primary spheroidal mirror with a thin correcting lens that removes spherical aberrations. The secondary mirror is placed in the center of the correcting lens, reflecting light through a hole made in the primary mirror. Not as famous as the Schmidt-Cassegrain telescope but common though is the Maksutov telescope that also uses a correcting lens with the primary mirror, this time their surfaces being concentric.

Observations in Other Wavelengths
For a detailed analysis of the sky, observations are also carried in other regions of the electromagnetic spectrum. Very popular and efficient are radio telescopes, developed mostly in the last century. A common problem for both radio and optical telescopes is the need for better resolution. We can derive the resolution of a telescope by using Rayleigh criterion, that states the resolving power is equal to the ratio of the incoming wavelength to the diameter of the aperture (times 1.22 for circular apertures). So for a good resolution we need a diameter as big as possible. The biggest radio telescope in the world is the Arecibo telescope from Puerto Rico that uses a huge dish of 305 m diameter. In order to solve the problem for resolutions, astronomers have developed a new technique called interferometry. The basic principal of interferometry is that by observing the same object with two distinct telescopes we can obtain a final image by "connecting" the two initial ones. Nowadays, the most efficient observatory that uses interferometry is the Very Large Array located near Socorro, New Mexico. It uses 27 telescopes placed in a "Y" shape, with 25 m aperture each. There also exists a technique called Very Long Baseline Interferometry (VLBI) that allows astronomers to resolve images over the size of continents. The biggest project of the century in this domain is the building of the Atacama Large Millimeter Array (ALMA), which will be using 66 telescopes placed in the Atacama desert of northern Chile.

Space-Based Observations
Because Earth-based observations are affected by extinction due Earth's atmosphere, observations carried out in space are more successful. We mention the Hubble Space Telescope (HST) that has a 2.4, f/24 primary mirror, the smoothest mirror ever constructed. The Hubble Space Telescope is placed on a low-orbit around Earth and because of the lack of atmosphere it can observe very faint objects. Another Space Telescope is the James Webb Space Telescope (JWST) which is planned to be launched in 2018. It will have a 6.5m primary mirror and it will orbit around a gravitation stable point on the Sun-Earth line known as the Second Lagrange Point (L2). Here the gravitational attractions due to both Sun and Earth balances the centrifugal force of an object set in motion around the Sun. This point has the special property that if an object is placed here, it is in equilibrium with respect to the Sun-Earth system. The second Lagrange Point lies on the line connecting Sun and Earth, on the other side of the Earth. So a telescope placed here will receive less thermal radiation, which will improve Infrared Observations.