Abstract
This is the first chapter of the third section. It describes the kinds of mathematical models usable by a mobile robot to represent its spatial reality, and the reasons by which some of them are more useful than others, depending on the task to be carried out. The most common metric, topological, and hybrid map representations are described from an introductory viewpoint, emphasizing their limitations and advantages for the localization and mapping problems. It then addresses the problem of how to update or build a map from the robot raw sensory data, assuming known robot positions, a situation that becomes an intrinsic feature of some SLAM filters. Since the process greatly depends on the kind of map and sensors, the most common combinations of both are shown.