One concept which is radically modified by the Principle of Relativity is that of simultaneity. Every-day experience indicates that the statement ``two events happened at the same time'' (i.e. they are simultaneous) is universal, and would be verified by any one looking into the matter. Thus I can say, ``I got home at the same time you got to work'' and nobody (usually) wonders about the consistency of such statement.
The surprising result is that two FBI agents looking into the matter but moving with respect to each other (and having very accurate clocks) would get conflicting answers. In order to illustrate this result we will consider two murder mysteries, one set in Victorian England which is analyzed using Newton's ideas, the other is set in outer space and is studied following Einstein's guidance.