Explore a comprehensive tutorial on real-time reachability in high-dimensional Hamilton-Jacobi PDEs. Delve into applications, traffic patterns, simulations, and hybrid systems with a focus on the SkyDo model. Examine reachability concepts, unsafe sets, non-anticipated strategies, and finite time horizons. Investigate the Hamilton-Jacobi-Isaacs equation, level set methods, and the Level Set Toolbox. Learn about control and disturbance in simulations. This lecture, presented by Claire Tomlin from the University of California, Berkeley, is part of the High Dimensional Hamilton-Jacobi PDEs Tutorials 2020 series at the Institute for Pure and Applied Mathematics, UCLA.