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This lecture covers cylindrical and spherical coordinates, as well as rotations in physics. It explains the geometric properties of cylindrical and spherical coordinates, their applications in describing motion with symmetry, and the concept of rotations in a direct mobile frame. The lecture also delves into the formulas of Poisson, symmetries in physics, polar and axial vectors, and their applications in physics. The instructor, Dr. Sylvain Bréchet from EPFL, provides detailed explanations and examples throughout the lecture.