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How to get the pure analytic solutions of the Partial Differential Equations (PDEs) ? What a hard challenge !... But solving these PDEs will be very useful for our human society. Among all these equations we find these of Navier - Stokes that describe the behavior of any kind of fluid as the water or the air, these of Maxwell that explains the electromagnetic phenomena as lightning bolts in the sky, and this of Schrodinger which is the first PDE to have explained the quantum world. Only various numerical solutions have been found for these equations. So, it became inevitable to create a new concept able to express their pure analytic solutions. Its name is «Gradient of time». What a surprising concept. Indeed, it gives by its existence, an indeniable proof of the way all the universe phenomena, are ruled by the relativity's laws, as it was proved by the genius Albert Einstein. This is why, the «Gradient of time» is also used in the actual book, to write thanks to the PDEs pure analytic solutions, an alternative theory of relativity.