## Abstract

The fundamental definition of the terminology that is known to us as *wave* consists of a series of examples of different situations, which we are referring to as waves. However, the one feature that is a common denominator for the type of waves is that they propagate in one or other directions, and they create some kind of “disturbance” in their path of their propagations; for example in case of water waves, we observe the elevation of water surface and in case of sound wave we experience pressure variations in its path of traveling, with a velocity characteristic of the medium the wave goes through. However, for us to be able to describe a wave we need a more definitive of describing the wave with the use of mathematics, and primarily the concept of partial differential equation-type scenarios, which goes beyond the level of most of any basic textbook. Thus, in this chapter we try to establish first of all what the wave is in general, and secondly describe each form or shape that these waves are produced both from classical and relativistic mechanics, as well as electrodynamics point of views. This approach allows us to identify mechanical wave, electromagnetic waves, and finally the quantum mechanical waves as well. Within each of these categories then we can establish types of wave and classify them such as soliton wave, scalar wave, plasma wave, and shock waves.

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