This master thesis deals with energy based control design in order to swing up and stabilise the Furuta pendulum. The laboratory model of this system was already used in [Angerer, Frauscher, Khor], where among others the method Interconnection and Damp- ing Assignment - Passivity Based Control (IDA-PBC) was treated and applied successfully. In a certain way, this method can be interpreted as a generalisation of the Method of Controlled Lagrangians, on which this thesis focuses mainly. Hence, one can surmise that using this method will lead to success too. To be able to treat both methods, the Euler-Lagrange as well as the Hamiltonian picture is required for describing mechanical systems (Chapter 2). Due to the fact that the Furuta pendulum is an underactuated system, the control design based on those methods leads to certain PDEs. These so-called Matching Conditions must be fulfilled in order that stabilisation can be achieved (Chapter 3). For the Method of Controlled Lagrangians, a special class of systems is introduced, where those Matching Conditions are simplified. Hence, we are talking about Simplified Match- ing Conditions and in further consequence a structure-preserving control law can be designed (Chapter 5). The Furuta pendulum is excluded of the mentioned special class because gyroscopic force terms occur there. Consequently, a control law which transforms the present system must be determined first (Chapter 4). By using these non-linear control laws, a far more extensive basin of attraction compared to linear control methods can be achieved. However, this methods are not suitable for a swing up too. Therefore, a required hybrid system should be designed (Chapter 6). For one thing, this consists of a control law where the physical energy of the system is forced to a desired energy level. For another thing, a stabilising controller based on the Method of Controlled Lagrangians is contained in the hybrid system. Every mentioned control method should be analysed and subsequently tested in simulations and on the real laboratory model.