Of all the great scientists of the world, Einstein is regarded as the greatest and also, the most loved. 

One of his greatest contributions to the field of science was the Special Theory of Relativity(STR), which he published in the year 1905. However, the STR starts with the Lorentz Transformation 

Similarly, many years before it was famous scientist Galileo Galilee who invented the Galilean Transformation. It proved to be the most approved transformation of that time.

The Galilean Transformation starts with two frames S and S’ where S’ moving with a constant velocity V along the x-axis. This was how Galileo started his famous transformation. Galilean Transformation equations are:    

    x’=x-Vt
    y’=y
    z’=z 
    t’=t         

The equation for x-axis is such that because the S’ frame moves in x-axis. However, the Inverse Galilean Transformation equations are:

   x=x’+Vt
   y=y’
   z=z’
t=t’

These sets of equations were used in that time. Moreover, the Galilean Transformation keeps acceleration invariant under it.

During the 19th century, the Electromagnetic Theory given by Maxwell was one of the most successful theory in Physics. Einstein being a great admirer of Maxwell was never satisfied with the fact that Maxwell’s Electromagnetic Theory was not invariant under Galilean Transformation. This however led Einstein to think and come up with Lorentz Transformation along with Lorentz.