This diploma thesis deals with the topic of mobile robots and describes the development of a mobile robot for localization and mapping of space. The second chapter gives examples of applications and presents the necessary sub-bases for successful autonomous navigation. The third chapter describes in more detail the process of mapping the environment and localization. These two subsystems are closely related and together we call them SLAM. In addition to mapping and the localization process, the route planning process is described in more detail, which aims to enable the mapping of the entire workspace. In addition to the theoretical approach of the mobile robot problem, the task of this paper has been to create an autonomous mobile robot that has the function of localization and mapping of space, described in the fourth chapter. The control of the developed mobile robot is based on an Arduino microcontroller that communicates wirelessly via bluetooth with android mobile devices. The task of the microcontroller is controlling the motors, ultrasonic sensors, gyroscope and other assemblies on the robot, and the task of the Android device is to make decisions about further movements of the robot and graphically present the robot's working environment based on information obtained from the microcontroller. In the fifth chapter, both program codes used to control this mobile robot are presented and explained. The last chapter presents the results of the mapping and localization process and addresses some problems of the selected mapping algorithm in addition to problems of locomotion and robot localization.