stingc

Geroch's "Relativity from A to B" is probably a good start. I haven't read it myself, but he is an excellent writer, and the description looks good.

A somewhat different kind of book is Taylor and Wheeler's "Spacetime Physics." This is more of a (very) introductory textbook written rather whimsically. The math is no more complicated than algebra, though.

One of the rarely advertised facts of science (especially physics) is that most of its progress hinges on formulating questions (and their answers) in just the 'right' way. Using one quantity/coordinate system/mathematical technique over another often makes a tremendous difference in one's intuition. And this is ultimately what guides experimental design and analysis, as well as theoretical explorations. Anyway, energy is one of those things that was found to be very useful a long time ago. Its utility has only increased since.

Energy is closely related to capacity to do work (or the amount of work required to prepare a system from some reference state). Work is in turn defined to be the action of a force over a distance. It therefore has units of newton-meters or foot-pounds. But the units of force are really mass*length/time^2 (think of F=ma). So work has units of mass*(length/time)^2 = mass*velocity^2. By definition, energy also has these units.

The reason that the concept of work requires that a force act over a distance is that things can sometimes exert forces on each other forever if there is no displacement. The chair you're sitting on right now is pushing you upwards to counteract the force of gravity pulling you down (otherwise you'd fall through it). Despite this, it clearly isn't doing any 'work' in the intuitive sense of that word.

The real justification, though, is that the total energy of an isolated system never changes. It turns out that this is actually due to the universe's 'temporal translation symmetry.' It can be proven that energy conservation is a consequence of the fact that the fundamental laws of physics don't care what time it is. This result is a special case of something called Noether's theorem. This states that every symmetry automatically implies the existence of a conserved quantity. Linear and angular momentum happen to be due to the translational and rotational symmetries of space, respectively.

Interestingly, these symmetries often disappear in curved spacetimes. Finding useful conservation laws becomes extremely tricky in general relativity.

Yes, all of this can be done with Lorentz transformations. I find them annoying, though. Everything you need can be derived much more elegantly from the Minkowski metric/invariant interval (a generalization of the Pythagorean theorem that connects spatial and temporal 'directions').