We define the only example of fully linear general relativity, for plane parallel (pp waves), where the Einstein equation reduces to a Poisson equation. We show, according to Penrose, that in the “Penrose limit,” when focusing in near a null geodesic, we find a pp wave. We show how to go between the “Rosen coordinates” and “Brinkmann coordinates” for the pp wave and give an example of the Penrose limit. Gravitational shockwaves are defined in flat space, leading to the Aichelburg–Sexl metric. General shock waves, shock waves generated by a graviton, and shockwaves in other backgrounds, are defined. We end with the Khan–Penrose interacting solution for two colliding shock waves.