In this paper an elaboration of the physical concept of inertia is presented and it leads to a definition of the Generalized Principle of Inertia and of inertial motions in the order of a wider view that considers also the presence of the gravitational field. At last the paper terminates with the examination of a few paradoxes of time that certainly represent evident contradictions inside theories that prove the existence of relativistic effects of time that would be generated by imaginary changes of spacetime due to the inertial speed.