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Arguably, no other musical instrument has had more of an impact on how music has evolved since the beginning of the twentieth century than the electric guitar. Conceived in the early 1930’s, the electric guitar became a necessity as jazz musicians sought to amplify their sound. Since then, it has evolved into a stringed musical instrument capable of a multitude of sounds and styles. It served as a major proponent in the development of rock and roll, as well as countless other genres of music.
The first electric guitars, designed by Rickenbacker Guitars, were hollow bodied instruments with simple designs and somewhat crude electronics. They employed the use of a pickup — a magnet wrapped in a coil of thin wire that transmits the vibrations of the guitar strings attached to standard acoustic guitars. As time passed, the first solid body guitars began to evolve thanks largely to an Epiphone Guitars luthier — or guitar maker — named Les Paul. The solid body guitar, also initially a crude design, allowed for a more ample sound and warmer tone than the hollow bodies.

Because the electric guitar is a stringed instrument, the best way to create sound from it is to transmit string vibration through magnetic pickups. Generally, there are two types of guitar pickups: single coil and humbucking. Single coil pickups are comprised of a single magnet wrapped in thin wire; they tend to create a bright sound that can be altered depending on its position on the guitar body. Unfortunately, these pickups are more susceptible to creating excess noise and feedback, known in the guitar world as ‘hum.’ These types of pickups came standard on the first production solid body electric guitars and on subsequent models for years thereafter.
Humbucking pickups were designed to counter the problem of the loud hum associated with single coil pickups. Humbucking pickups are composed of two magnets set opposed to each other to cancel out the feedback associated with single coil pickups, effectively bucking the hum, so to speak. The more powerful humbucking pickups tend to produce a warmer and deeper tone than single coils, and their tone can also be altered depending on their position on the guitar body.

The electric guitar, like most electric instruments, must be used in conjunction with an amplifier that will transmit the signal through a speaker, thus creating the louder sound. Though not exclusively, electric guitars almost always employ the use of an external amplifier and speaker system. There are several different types of amps, but the most common are combo amps, which combine the amplifier providing the power and the speaker providing the sound in a single casing, and amp and cabinet set-ups, which separate the amplifier from the speaker or speakers. Both setups are great for different settings, so be sure to choose the one that will suit your needs the best.
Because sound varies depending on the shape, size, material, and components, it helps to try out several different electric guitar and amp setups before choosing one for yourself. Guitars vary immensely in price range, so be sure to decide what your needs are before purchasing.

From: http://www.wisegeek.com/what-is-an-electric-guitar.htm