The basic question of Simultaneous Localization and Mapping (SLAM) is whether a mobile robot placed in an unknown location and environment is capable of gradually creating a consistent map of its surroundings while simultaneously determining its own position. SLAM has been theoretically formulated and solved in various variations. It has been implemented in indoor and outdoor robots, underwater systems, automobiles, unmanned aerial vehicles, and household appliances. The theoretical and conceptual level of the SLAM basic question can be considered solved. This solution is a significant achievement in the field of robotics; however, there are still significant limitations in practical applications, particularly in creating and utilizing detailed perception maps as part of the SLAM algorithm. The relevance of the SLAM problem has not diminished from its inception to the present day. Despite numerous studies, simulations, and real-world experiments, new algorithms and methods are still being invented or supplemented with the aim of achieving a complete solution. For this reason, the topic of SLAM is interesting for indepth research, as it provides an opportunity to participate in finding a solution to the problem. The main goal of this work is to explore simultaneous localization and mapping algorithms and examine the most popular SLAM methods. Utilizing the acquired knowledge, other goal is to develop a prototype of a low-cost SLAM radar device. The thesis formulates what SLAM is, describes its structure and methods, problems, as well as the latest research trends and algorithms. Visual and LiDAR SLAM methods, their algorithms, application modes, key limitations, and development directions are extensively examined and described. In the practical part, a radar device based on Time-of-Flight (TOF) sensor is developed, which allows determining the distance to objects within its field of view.