This doctoral thesis deals with an open subproblem of robot navigation, namely simultaneous localization and mapping (SLAM) in three-dimensional space. The goal is to develop a system which is capable of localizing a mobile robot in a reliable way and at the same time reconstruct its environment as a three-dimensional map. Besides enabling robot navigation in 3D, such a map could be of great importance for higher-level robotic tasks, like scene interpretation or manipulation as well as visualization purposes in general, which are required in surveying, architecture, urban search and rescue and others. The third dimension is challenging. Firstly, sensors providing three-dimensional data have to be found which suit the requirements of mobile robots and therefore have to be limited in size and power consumption. For this work, two sensors have been considered: the Swiss Ranger from CSEM (Swiss Center for Electronics and Microtechnology) and a custom-built range sensor based on a commercially available 2D laser scanner from SICK. Both are active sensors relying on measuring the time-of-flight of the emitted light. After calibration and error analysis it was concluded that the Swiss Ranger is less suited for localization and mapping than the rotating laser scanner due to its noisy data and limited field of view. It was therefore not further considered in the ensuing work. As a single 3D scan generated by the rotating laser scanner can be composed of many tens of thousands of data points and the robot takes dozens of scans during a mission, it is necessary to compress the raw data to visualize and process it efficiently. The method chosen in this work is to use a feature-based representation, which enables detailed and, at the same time, compact and informative environment reconstruction. The chosen features are planar segments, whose probabilistic representation and extraction are described, results of the SLAM algorithm are shown. With the aid of an Extended Kalman Filter (EKF) the pose of the robot and the location of the different planar segments – considering their uncertainty – can be estimated in an incremental way. The framework defined by the SPmodel (Symmetries and Perturbations Model) is used, allowing to represent and process various uncertain geometric models. The approach is validated through different experiments with a mobile robot in an office environment.