A mobile robot system with the ability to perform mapping and localisation has the potential to be applied in various applications such as indoors and outdoors, known and unknown, offiine and real time as well as static and dynamic environments. At present, implementations for these mobile robots utilise ultrasonic, infrared, RFID and similar sensing modalities. However, such implementations have severe limitations including the need of reference for localisation, high computational requirements, slow processing due to sensing requirements and may also be less accurate. Hence, this thesis proposes the utilisation of single laser range finder for mobile robot mapping and localisation system for static. The laser range finder used is the RP lidar, and its utilisation enables the mobile robot to perform the mapping and localisation in known, unknown, as well as structured indoor environments. The implementation of the laser range finder negates the need of multiple sensing modalities to perform the mapping and localisation. A remote control mobile robot was augmented with a single RP Lidar laser range finder and transformed to enable it to function autonomously. The mapping and localisation algorithm were developed using scan-matching approach and exploits the high-speed scanning of the RP Lidar. KNN and rule-based algorithm were implemented for decision making and the testing was performed both in simulation and as well as real world in real time. The evaluations of the proposed system were performed in static and structured indoor environments. The results of the testing showed that the mobile robot system was able to perform self-location with high accuracy, 90% and above. Also, it was able to navigate to the target location in static dynamic environments. The mobile robot mapping and localisation system with the use of single RP lidar laser range finder was able to replace the multiple sensing modalities approach and it was able to perform with high accuracy for static environments.