This paper presents a unified theory to deal with when, why and how a sharp acidization dissolution front (ADF), which is represented by the porosity distribution curve, can take place in an acidization dissolution system composed of fluid-saturated porous rocks. The theory contains the following main points: (1) A reaction rate of infinity alone can lead to a sharp ADF of the Stefan-type in the acidization dissolution system. This sharp front is unstable when permeability in the downstream region is smaller than that in the upstream region. (2) For a finite reaction rate, when the acid dissolution capacity number approaches zero, the ADF can have a sharp profile of the Stefan-type either on a much smaller time scale or on a much larger time scale than the dissolution time scale. In the former case, the ADF may become unstable on a much larger time scale than the transport time scale, while in the latter case, it may become unstable if the growth rate of a small perturbation is greater than zero. (3) On the dissolution time scale, even if both the reaction rate is finite and the acid dissolution capacity number approaches zero, the profile of an ADF may not be sharp because it is in a transient state. In this case, not only can an ADF change its profile with time, but also its morphology can grow if the growth rate of a small perturbation is greater than zero. Due to the involvement of both the change rate and the growth rate of the ADF profile, it is necessary to conduct a transient linear stability analysis for determining whether or not a time-dependent ADF is stable in the acidization dissolution system.