Complete Special Relativity

Postulates

The laws of physics are the same in inertial frames, and the speed of light is invariant.

Lorentz Transformations

For motion along $x$,

$$t'=\gamma\left(t-\frac{vx}{c^2}\right), \qquad x'=\gamma(x-vt).$$

Spacetime

The invariant interval is

$$ds^2=-c^2dt^2+dx^2+dy^2+dz^2.$$