nitsuj said:
I like the perspective it's the geometry of spacetime; however that is one step after the most favored irreducible reply, that c is invariant. Am surprised no one mentioned causality. That's a fun one to think of as being the cause of time dilation / length contraction.
For a simply put book on SR, Relativity (a brief insight) by Russell Stannard is one I like. He put's a fair amount of emphasis on measurement (in turn perspectives); which I find important when developing an understanding of the concept in general.
I would have mentioned causality and other things but I was too busy to comment and the thread has gone on for a while now.
But since you mentioned causality...
I would say that the big idea in relativity and spacetime, at the deepest level, isn't the Lorentz group but it is the causal structure.
And there are some interesting papers along these lines.
"Causality Implies the Lorentz Group"
Journal of Mathematical Physics 5, 490 (1964);
https://doi.org/10.1063/1.1704140
E. C. Zeeman
"A contribution to chronogeometry"
Canad. J. Math. 19(1967), 1119-1128
https://cms.math.ca/10.4153/CJM-1967-102-6
A. D. Alexandrov
"Zeeman topologies on space-times of general relativity theory"
Communications in Mathematical Physics, October 1976, Volume 46, Issue 3, pp 289–307
https://doi.org/10.1007/BF01609125
Rüdiger Göbel
and likely what first inspired this line of thinking was
"The Absolute Relations of TIme and Space" (1921) and "The Geometry of Time and Space" (1936)
https://archive.org/search.php?query=creator:"Robb,Alfred+A."
A.A. Robb (
https://en.wikipedia.org/wiki/Alfred_Robb )
where he used the notion of "after" (a partial order relation) to try to "derive" Minkowski spacetime.
Robb introduced the notion of "rapidity" is relativity.
His "Optical Geometry of Motion" (1911)
https://archive.org/details/opticalgeometryo00robbrich is surprisingly insightful for 1911, just a few years after Minkowski (1907) and Einstein (1905). You can see aspects of the radar method in it.