The Direct Method of Lyapunov is often employed to prove the stability of nonlinear dynamic systems. During this talk we'll explore the Lyapunov Theorem as used in the State Domain used to model physical systems. We'll also see how the Lyapunov Stability Theorem can be used to design a controller for certain types of systems using Full State Feedback. Finally, with regards to equations of motion that govern the rotational motion of spacecraft, we'll compare the Full State Feedback method to the Direct Adaptive Control method.