I have these past few weeks been steadily studying the different aspects of the theory of Special Relativity. I started with the Lorentz transformations and, thinking I understood them, went along and studied other parts of the theory. However, along the line it has become apparent to me that my understanding of the transformations is a bit blurry, especially when I got around to using the inverse Lorentz transformations, and I'm hoping someone could help me straighten things out. As I see it, there are four "different" sets of co-ordinates when dealing with two reference frames S and S' moving relative to each other: - S co-ordinates as seen from S - S co-ordinates as seen from S' - S' co-ordinates as seen from S' - S' co-ordinates as seen from S Now, I'd like to clear up for myself once and for all, between which of these the Lorentz transformations transform. And also, what purpose do the inverse transformations serve when the situation is symmetrical and reversible? If anyone could provide me with a clear definition, I'd much appreciate it.