Abstract. This book summarises, with additions and revisions, the contents of several papers on Relativity and other topics that I published in the International Journal of Innovation in Science and Mathematics. In particular, the hypothesis is proposed that the Michelson-Morley experiment can be explained by abolishing the second postulate of relativity and the contraction of lengths. The concept of space-time and the relativity of simultaneity are also rejected. To explain the Michelson-Morley experiment it is hypothesised that the speed of light can slow down as a function of the motion of its source with respect to a privileged system. This hypothesis, in line with Occam's razor, unlike Einstein's elegant mathematical formulation of Relativity, proposes a much less elaborate scenario, but without the paradoxes arising from that formulation.Some considerations on Astronomy are also made: in fact Halton Arp's now marginalised theory of the stationary universe is partially reconsidered. Indeed, explaining the results of the Michelson-Morley experiment through the variability of the speed of light opens up scenarios other than those designed by the Big Bang Theory.....