Transformations of space and time between inertial systems are set up by starting from two empirically based assumptions: (1) The two-way velocity of light is the same in all inertial systems; (2) Clock retardation takes place with the usual velocity-dependent factor when clocks move with respect to an isotropic reference frame. The transformations thus obtained contain a free parameter e1, the coefficient of x in the transformation of time. The Theory of Special Relativity is recovered for a particular choice of e1. Different values of e1 correspond to different theories of space and time, which are to a large extent empirically equivalent. We show that Michelson type experiments, aberration, occultation of Jupiter\'s satellites, and radar ranging of planets are insensitive to the choice of e1. Several other experiments lead to the same conclusion. An exception is discussed in Part II.