Control theory makes significant progress, since nonlinear systems and differential geometry have been brought together about 30 years ago. The main advantage is that a description of the control system is avalaible, which does not require the choice of special coordinates. Now, many important properties of dynamic systems can be characterized in a geometric way. Within this framework nonlinear systems are considered as geometric objects, defined on smooth manifolds. E.g., a nonlinear control system can be identified with a submanifold of a certain geometric structure. Non observable or non accesible systems generate a foliation, and so on. This talk gives an introduction to the geometric description of nonlinear control systems, described by a set of ordinary differential equations. It starts with a short overview, where time invariant and time variant systems with or without control input are characterized by its geometric properties. At the same time a short introduction to the required mathematical tools will be presented. Having this preliminaries at our disposal we develop the concept of accessibility and observability by geometric ideas. It will turn our that this approach is not confined to explicit systems, on the contrary it can be generalized to more complex ones. Fortunately these methods are not only useful for the analysis of systems, where equivalence means that solutions of one system can be transformed to solutions of the other and vice versa. Using the idea that a dynamic system is also a certain sybmanifold, we show that equivalent systems describe the same submanifold in different coordinates only. From a systems designer’s point of view, it is important to construct equivalent systems such that the control loop design can be reduced to an already solved problem Finally, this talk finishes with an industrial application of the present methods. The hydraulic gap control of stands in steel rolling mills is a challenging task because of the intrinsic nonlinear behaviour of these systems. We present new design ideas and controllers and prove the performance by simulations and measurements taken in mills located in the US and Europe.