Lorentz Invariance, the main ingredient of Special Relativity, is one of the pillars of modern physics. Though Special Relativity has been replaced by General Relativity, Lorentz Invariance is still valid locally. All physical fields have to obey the laws of local Lorentz Invariance. This is also the reason why gravity within the theory of General Relativity has to be described by the metric tensor. Here we give a short introduction into the early experiments and show that they disproved the exact validity of the Galilean framework for the description of classical mechanics. After a short summary of Special Relativity, the procedure of synchronization is analyzed. It is emphasized that no experiment should depend on the synchronization. Otherwise it might be possible to simulate or compensate effects by choosing another synchronization. Accordingly, the requirement of synchronization independence is a guideline for the choice of appropriate measurable quantities which then reveal relativistic physics in an unambiguous manner. Examples are given. In a subsequent article the modern experiments implementing this kind of notions will be discussed. Also some remarks are made on the importance of Lorentz Invariance in daily life. Finally we comment on possible violations of Lorentz Invariance and their measurability.