This course covers the fundamentals of groups, fields, and vector spaces; fundamentals of differential geometry including Lie groups (and their tangent bundles), Lie algebras, and the exponential map; Review of classical mechanics (Newtonian and Eulerian); Introduction to dynamic modeling formulation in geometric mechanic framework accounting for translation-rotation couplings in body motions; Lagrangian and Hamiltonian developments of variational integrator to preserve system geometric properties; Fundamentals of Lyapunov-based geometric theory of nonlinear control and Morse- Lyapunov stability analysis of the rigid body motions; Applications to formation flight, consensus of rigid bodies, multiple-DOF systems, etc.