  In this paper we treat the pre-ionisation problem in shocks over the velocity
range $10 < v_{\rm s} < 1500$\,km/s in a self-consistent manner. We identify
four distinct classes of solution controlled by the value of the shock
precursor parameter, $\Psi = {\cal Q}/v_s$, where ${\cal Q}$ is the ionization
parameter of the UV photons escaping upstream. This parameter determines both
the temperature and the degree of ionisation of the gas entering the shock. In
increasing velocity the shock solution regimes are cold neutral precursors
($v_s \lesssim 40$\,km/s), warm neutral precursors ($40 \lesssim v_s \lesssim
75$\,km/s), warm partly-ionized precursors ($75 \lesssim v_s \lesssim
120$\,km/s), and fast shocks in which the pre-shock gas is in photoionisation
equilibrium, and is fully ionized. The main effect of a magnetic field is to
push these velocity ranges to higher values, and to limit the post-shock
compression. In order to facilitate comparison with observations of shocks, we
provide a number of convenient scaling relationships for parameters such as
post-shock temperature, compression factors, cooling lengths, and H$\beta$ and
X-ray luminosity.
