James, Matthew R.These tutorial notes discuss the basic ideas in the theory of controllability and observability for nonlinear control systems. The theory treated is primarily due to Hermann and Krener. The first section gives a short overview of the issues, followed by section 2 which reviews distributions, codistributions, and the Frobenius Theorem. Section 3 deals with controllability. Chow's Theorem is presented, before beginning the Hermann-Krener theory. Finally, section 4 discusses the Hermann-Krener formulation of observability. A number of examples and illustrations are provided.en-USTechnical Report