The paper presents an approach to the problem of universal adaptive stabilization for discrete-time systems by means of switching controllers, as previously developed in different ways by Martensson (1985), Fu-Barmish (1986), Miller-Davison (1989), for continuous-time systems. It is assumed that the plant is linear, time-invariant and can be stabilized by a feedback compensator of known structure, so that the task of the switching algorithm is to search the space of possible controller parameters until stability is achieved. Since the search has to be undertaken on an infinite set, dense in the parameter space, the algorithm is designed so that, in the absence of disturbances, the switching will eventually terminate and the system will then asymptotically approach its equilibrium state. Moreover, by utilizing the internal model principle, the adaptive stabilizer can be embedded in a control scheme to track reference signals with known dynamic properties. Modifications are then considered, so as to allow for the presence of disturbances. (5 pages)