This article is devoted to the key concept of modern electrodynamics—the invariance of the speed of light. The general principle of relativity is considered in detail. Some critical remarks to the relativistic invariance and to the Lorentz transformations are presented. The general invariance of Maxwell equations is discussed. Different theoretical expectations for possible results of Michelson-Morley experiment and some physical consequences are considered. Some critical remarks to the notion of the light speed and its constancy are given. The relativistic law for velocity addition, including strangeness of a noncollinear addition and a superluminal motion, is discussed. Critical analysis of two works which proof the need for existence of an invariant velocity is consequentially made.Producción Científica de la Universidad Autónoma de Zacatecas UAZ