Nonlinear geometric control and observer design methods for multi-input nonlinear systems. Differential geometric tools including manifolds, Lie derivatives, Lie brackets, distributions, and the Frobenius Theorem. Conditions for local and global exact and partial state feedback linearization. Output tracking design using input-output state feedback linearization. Local and global nonlinear observer design using exact error linearization. Output feedback control including output feedback linearization and output feedback stabilization based on normal forms. Design methods learnt in this course are implemented on a real physical system.