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An amplifier takes a signal and boosts the power behind it. There are basically two kinds of amplifiers: Preamplifiers, and Power amplifiers. Preamps used to be useful a long time ago, but now they mainly serve to switch between different line level inputs, and control their volume. The preamp increases the voltage of the signal, but not the current. The power amp, on the other hand, increases the current enough to drive loudspeakers. The Lepai LP-2020A+ is a very cheap Power amplifier that is often recommended to people who are just starting out in the world of audio. The problem with this amp is that it is on the low side of the amount of power, and there is only one Line Level input on there, which means you would need some means to switch between audio sources, or only listen to audio from one source.
Phono Pre Amp
There is one case where pre amplification is still useful: Phonographs, AKA record players. The signal coming from the cartridge on a turntable is measured in millivolts, so before it goes to the power amplification stage, it must go to pre amplification. A phono pre amp also applys the RIAA equalization curve to the signal, which makes the record sound the way that it should. You cannot plug phono level inputs into a line level input in a power amplifier. If you do, it won't sound right. A common phono pre amp for beginners is the ART DJPRE II.