Simultaneous Localization and Mapping (SLAM) has been considered by literature the holy grail of the robotics because of many aspects, first above all the enhanced ability of generic unmanned vehicles to move in an unknown and unstructured environment. Anyway, SLAM is a chicken-or-egg problem since for localization a map is needed and for mapping the information about the precise position is required, hence the two aspects cannot be approached independently, indeed their reciprocal relationship determine the real core of the matter. The work aims at describing what SLAM is and how it can be implemented from a theoretical point of view.