Although Einstein is known as a Physicist and generally all round nice guy, rather than a cycles researcher, his work profoundly affects the study of electromagnetic waves which are intimately connected with cycles.
Special relativity is all about the correct application of Maxwell's equations when there is motion of the parts, and Maxwell's equations are pure wave equations. Without special relativity, everyone was actually doing their calculations of bodies in motion wrongly - in effect assuming that the speed of light is infinite. This is based on our intuition which deceives us because we do not normally ever experience velocities at which it is wrong. Einstein's brilliance was to break through the misconceptions of the human mind and find out the correct way to apply electromagnetism when there is high speed motion.
In general relativity, he likened the effects of gravity to acceleration and so was able to include matter into the sphere of Maxwell's equations also. This is very important because before that they were only really about electromagnetic waves which is only part of the story of nature.
His result was that matter creates distortions in the fabric of space which must as a result be considered together with time as space-time as it is not possible to find a unique perspective which totally seperates the two.
This distortion means that Maxwell's equations become non-linear equations because matter, and in fact all energy, creates distortions which influence the path of waves. Although it is usually taught that the speed of light is constant, with special relativity the result is really that light is bent by energy concentrations, be they matter or electromagnetic waves, and this can equally be interpreted as variation in the velocity of light.
Because any fundamental explanation of the nature of cycles is equally about waves, the lessons of relativity provided by Einstein are very important for understanding the deepest aspects of cycles theory. In fact the equation of general relativity is a wave equation.