Simultaneous Localization and Mapping (SLAM) is one of the most widely researched areas of Robotics. It addresses the mobile robot problem of generating a map without prior knowledge of the environment, while keeping track of its position. Although technology offers increasingly accurate position sensors, even small measurement errors can accumulate and compromise the localization accuracy. This becomes evident when programming a robot to return to its original position after traveling a long distance, based only on its sensor readings. Thus, to improve SLAM s performance it is necessary to represent its formulation using probability theory. The Extended Kalman Filter SLAM (EKF-SLAM) is a basic solution and, despite its shortcomings, it is by far the most popular technique. Fast SLAM, on the other hand, solves some limitations of the EKFSLAM using an instance of the Rao-Blackwellized particle filter. Another successful solution is to use the DP-SLAM approach, which uses a grid representation and a hierarchical algorithm to build accurate 2D maps. All SLAM solutions require two types of sensor information: odometry and range measurement. Laser Range Finders (LRF) are popular range measurement sensors and, because of their accuracy, are well suited for odometry error correction. Furthermore, the odometer may even be eliminated from the system if multiple consecutive LRF scans are matched. This works presents a detailed implementation of these three SLAM solutions, focused on structured indoor environments. The implementation is able to map 2D environments, as well as 3D environments with planar terrain, such as in a typical indoor application. The 2D application is able to automatically generate a stochastic grid map. On the other hand, the 3D problem uses a point cloud representation of the map, instead of a 3D grid, to reduce the SLAM computational effort. The considered mobile robot only uses a single LRF, without any odometry information. A Genetic Algorithm is presented to optimize the matching of LRF scans taken at different instants. Such matching is able not only to map the environment but also localize the robot, without the need for odometers or other sensors. A simulation program is implemented in Matlab to generate virtual LRF readings of a mobile robot in a 3D environment. Both simulated readings and experimental data from the literature are independently used to validate the proposed methodology, automatically generating 3D maps using just a single LRF.