A unified theory of the mirror instability in space plasmas is developed. In the standard quasi-hydrodynamic approach, the most general mirror-mode dispersion relation is derived and the growth rate of the mirror instability is obtained in terms of arbitrary electron and ion velocity distribution functions. Finite electron temperature effects and arbitrary electron temperature anisotropies are included. The new dispersion relation allows the treatment of more general space plasma equilibria such as the Dory--Guest--Harris (DGH) or Kennel--Ashour-Abdalla (KA) loss cone equilibria, as well as distributions with power law velocity dependence that are modeled by the family of κ-distributions. Under these conditions, we derive the general kinetic mirror instability growth rate including finite electron temperature effects. As for an example of equilibrium particle distribution, we analyze a large class of κ to suprathermal loss cone distributions in view of application to a variety of space plasmas like the solar wind, magnetosheath, ring current plasma, and the magnetospheres of other planets.