SLAM is an approach deployed in robotics to develop autonomous mobile robots. These robots have been deployed in numerous fields such as manufacturing, aerospace navigation, and other areas deemed dangerous to humans. SLAM techniques have made these robots to operate without necessarily having the prior maps, a shortcoming of the current robots which require prior maps. Several SLAM approaches exist, but EKF has been seen to possess all the useful features of convergence and consistency. Via SLAM, concurrency between localisation and mapping has been made possible. An EKF SLAM algorithm has been presented in this thesis, which was implemented in a two-wheeled mobile robot. The robot autonomously navigated in a structured indoor environment, while simultaneously building a map and localising itself within that map. A 360 degrees LiDAR was used to measure the range and bearing of the surroundings and an ultrasound sensor was used to avoid the obstacles. Furthermore, the algorithm was implemented using Python 3.