Understanding Relativity is a textbook — the exercises at the end of each chapter are a giveaway — but one that is close in many ways to works of popular science. It doesn't shy from equations or mathematics, but it assumes only basic algebra and trigonometry, an understanding of what a vector is, and simple mechanics — no calculus and no electromagnetism. It begins with Galilean relativity and the Michelson-Morley experiment, then presents the basic postulates of relativity, Lorentz transformations, space time diagrams (including Loedel diagrams, which were new to me), and some of the standard "paradoxes". This is all explained clearly, with expansive explanations which avoid repetition. A brief account of relativistic mechanics (simple collision problems, the energy-momentum 4-vector) and chapters on general relativity and cosmology follow.
It's not easy to put myself in the shoes of someone encountering relativity for the first time. I think, however, that Sartori's account would work well for anyone with the appropriate background. It has the simplicity and readability I associate with the best popular science, combined with just enough quantitative mathematics and logical rigor — enough to give it a depth that would otherwise be impossible, but not so much as to obscure the basic ideas. Understanding Relativity would be suitable for a university course aimed at non-physics majors — with its good treatment of the historical background, students studying history and philosophy of science are one obvious audience. It is also within the reach of bright high school students or anyone else with equivalent mathematics and physics.