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Lorentz transformation (LT) can be explained in two ways Special Lorentz transformation (SLT) and Most general Lorentz transformation (MGLT). It has wide applications in Special and General Relativity, Relativistic Electrodynamics and Relativistic Quantum Mechanics. When the motion is not one dimensional we use MGLT. The calculations of different problems are complex if we use MGLT. Our research group has developed another three types of MGLTs called Quaternion Lorentz transformation, mixed number Lorentz transformation (MNLT) and Geometric product Lorentz transformation to overcome this problem. We have studied different properties of these different types of LTs and observed that the MNLT satisfies all the properties that we have studied. We have also studied some applications of different types of LTs such as Mocanu Paradox, Wigner rotation, relativistic aberration, relativistic Doppler’s effect etc. We have seen that for general case MNLT gives better results than any other LT. We have written this work for the researchers of Applied Mathematics, Mathematical Physics and the Master’s Students of the Universities in the world.