The approach presented here is based on the use of algebraic methods which are intrinsically linear, rather than differential geometric methods. This allows the exposition to remain simple from a mathematical point of view, and accessible for those with an understanding of linear control theory. It is divided into three parts: Part 1 is devoted to mathematical preliminaries and to the development of tools and methods for system analysis. Part 2 is concerned with solving specific control problems, including disturbance decoupling, non-interactive control, model matching and feedback linearization problems. Part 3 introduces differential algebraic notions and discusses their applications to nonlinear control and system theory. There are examples to illustrate theoretical results.