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In this paper, we consider the problem of autonomous navigation with a micro aerial vehicle (MAV) in indoor environments. In particular, we are interested in autonomous navigation in buildings with multiple floors. To ensure that the robot is fully autonomous, we require all computation to occur on the robot without need for external infrastructure, communication, or human interaction beyond high-level commands. Therefore, we pursue a system design and methodology that enables autonomous navigation with real time performance on a mobile processor using only onboard sensors. Specifically, we address multi-floor mapping with loop closure, localization, planning, and autonomous control, including adaptation to aerodynamic effects during traversal through spaces with low vertical clearance or strong external disturbances. We present experimental results with ground truth comparisons and performance analysis.