Errors in cyber-physical systems can lead to disastrous consequences. Classic examples date back to the Therac-25 radiation incidents in 1987 and the Ariane 5 rocket crash in 1996. More recently, Toyota's unintended acceleration bug was caused by software errors, and certain cars were found vulnerable to attacks that can take over key parts of the control software, allowing attackers to even disable the brakes remotely. Pacemakers have also been found vulnerable to attacks that can cause deadly consequences for the patient. To reduce the chances of such errors happening, this project investigates the application of a technique called Foundational Verification to cyber-physical systems. In Foundational Verification, the system being developed is proved correct, in full formal detail, using a proof assistant. The main intellectual merit of the proposal is the attainment of previously unattainable levels of safety for cyber-physical systems because proofs in Foundational Verification are carried out in complete detail. To ensure that the techniques in this project are practical, they are evaluated within the context of a real flying quadcopter. The project's broader significance and importance is the improved correctness, safety and security of cyber-physical systems. In particular, this project lays the foundation for ushering in a new level of formal correctness for cyber-physical systems. Although the initial work focuses on quadcopters, the concepts, ideas, and research contributions have the potential for transformative impact on other kinds of systems, including power-grid software, cars, avionics and medical devices (from pacemakers and insulin pumps to defibrillators and radiation machines).