One of the biological mechanisms that has so far been poorly understood is the ability of the brain to form representations of primary sensory experiences at increasingly higher levels of abstraction. At many lower perceptual levels, sensory information first becomes represented in topographically ordered sensory maps. In these maps neurons become tuned in a regular manner to simple stimulus features, such as amplitude, frequency, or direction of sound. In this paper it is shown that a model, originally devised by Kohonen for the understanding of the self-organized formation of such "lower-level maps," can also explain the formation of more abstract maps, such as adaptive maps for use in motor control, or maps in which, during a learning stage, the neurons become tuned in an orderly fashion to aspects of the semantic meaning of words. The actual presence of such maps in the brain is speculative at present, but many maps of simpler type have been found. It is argued that the process of the adaptive formation of maps may offer a way to a more unified understanding of many aspects of information processing in the brain.