In this thesis, we present an experimental analysis of several methods in the simultaneous localization and mapping (SLAM) literature. The mapping and localization methods have been simulated and tested on a quadruped robot. Each algorithms are LIDAR-based, hence we are implemented both three and six degree-of-freedom SLAM without using any other information except for the pointcloud. For every approch we perfomed an analysis about the mapping accuracy, the path accuracy and the computational effort. Moreover we applied the Monte Carlo localization to globally determine and track both the 3D and 6D pose estimation produced by the previouses methods. We present simulated as well as real-world experiments with the quadruped robot and thoroughly evaluate the best approch while the robot moves.