Micro aerial vehicles, such as multirotors, are particularly well suited for the autonomous monitoring, inspection, and surveillance of buildings, e.g., for maintenance or disaster management. Key prerequisites for the fully autonomous operation of micro aerial vehicles are real-time obstacle detection and planning of collision-free trajectories. In this article, we propose a complete system with a multimodal sensor setup for omnidirectional obstacle perception consisting of a 3D laser scanner, two stereo camera pairs, and ultrasonic distance sensors. Detected obstacles are aggregated in egocentric local multiresolution grid maps. Local maps are efficiently merged in order to simultaneously build global maps of the environment and localize in these. For autonomous navigation, we generate trajectories in a multi-layered approach: from mission planning over global and local trajectory planning to reactive obstacle avoidance. We evaluate our approach and the involved components in simulation and with the real autonomous micro aerial vehicle. Finally, we present the results of a complete mission for autonomously mapping a building and its surroundings.