The present thesis is concerned with the modeling and representation, as well as the control and analysis, of systems with distributed parameters based on differential-geometric methods. Since a large number of technical processes belong to this system class, which are mathematically described by partial differential equations, it constitutes an exciting but also challenging field of research. Unlike their counterparts, systems with lumped parameters, these systems not only have a temporal dependency but also a spatial one. Some examples for distributed-parameter systems are: the elastic deformation of lightweight structures in machinery and plant engineering, as well as thermal processes in the steel and plastic industry. Due to the rapid development of information technology and the nowadays almost unlimited computational power, but also because of the increasing demands with respect to, e.g., quality and productivity, the theory and practice of distributed-parameter systems have enjoyed great popularity among researchers in the last decades, even though the evolution of the mathematical theory of partial differential equations already started in the late seventeenth century. However, distributed-parameter systems are still considered as sophisticated, and an unified mathematical theory for the systematic description and investigation of their characteristics is not yet available. That is, the mathematical framework as well as the control concepts are zoologically adapted to the particular type of equation. It is therefore the aim of this thesis to exploit differential-geometric methods in order to analyze distributed-parameter systems, and to show their applicability to control engineering problems. To this end, the present thesis is divided into three main parts.